Communications in Contemporary Mathematics最新文献

{"title":"Moduli spaces of ℤ/kℤ-constellations over 𝔸2","authors":"Michele Graffeo","doi":"10.1142/s0219199724500196","DOIUrl":"https://doi.org/10.1142/s0219199724500196","url":null,"abstract":"","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140717597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sharp spectral gap estimates for higher-order operators on Cartan–Hadamard manifolds","authors":"Csaba Farkas, Sándor Kajántó, Alexandru Kristály","doi":"10.1142/s0219199724500135","DOIUrl":"https://doi.org/10.1142/s0219199724500135","url":null,"abstract":"<p>The goal of this paper is to provide sharp spectral gap estimates for problems involving higher-order operators (including both the clamped and buckling plate problems) on Cartan–Hadamard manifolds. The proofs are symmetrization-free — thus no sharp isoperimetric inequality is needed — based on two general, yet elementary functional inequalities. The spectral gap estimate for clamped plates solves a sharp asymptotic problem from [Q.-M. Cheng and H. Yang, Universal inequalities for eigenvalues of a clamped plate problem on a hyperbolic space, <i>Proc. Amer. Math. Soc.</i><b>139</b>(2) (2011) 461–471] concerning the behavior of higher-order eigenvalues on hyperbolic spaces, and answers a question raised in [A. Kristály, Fundamental tones of clamped plates in nonpositively curved spaces, <i>Adv. Math.</i><b>367</b>(39) (2020) 107113] on the validity of such sharp estimates in high-dimensional Cartan–Hadamard manifolds. As a byproduct of the general functional inequalities, various Rellich inequalities are established in the same geometric setting.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140573507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Complete CMC-1 surfaces in hyperbolic space with arbitrary complex structure","authors":"Antonio Alarcón, Ildefonso Castro-Infantes, Jorge Hidalgo","doi":"10.1142/s0219199724500111","DOIUrl":"https://doi.org/10.1142/s0219199724500111","url":null,"abstract":"<p>We prove that every open Riemann surface <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>M</mi></math></span><span></span> is the complex structure of a complete surface of constant mean curvature <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mn>1</mn></math></span><span></span> (<span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">CMC-1</mtext></mstyle></math></span><span></span>) in the three-dimensional hyperbolic space <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℍ</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span><span></span>. We go further and establish a jet interpolation theorem for complete conformal <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">CMC-1</mtext></mstyle></math></span><span></span> immersions <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>M</mi><mo>→</mo><msup><mrow><mi>ℍ</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span><span></span>. As a consequence, we show the existence of complete densely immersed <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">CMC-1</mtext></mstyle></math></span><span></span> surfaces in <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℍ</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span><span></span> with arbitrary complex structure. We obtain these results as application of a uniform approximation theorem with jet interpolation for holomorphic null curves in <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℂ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy=\"false\">×</mo><msup><mrow><mi>ℂ</mi></mrow><mrow><mo stretchy=\"false\">∗</mo></mrow></msup></math></span><span></span> which is also established in this paper.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140573461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Shadowing, Hyers–Ulam stability and hyperbolicity for nonautonomous linear delay differential equations","authors":"Lucas Backes, Davor Dragičević, Mihály Pituk","doi":"10.1142/s0219199724500123","DOIUrl":"https://doi.org/10.1142/s0219199724500123","url":null,"abstract":"<p>It is known that hyperbolic nonautonomous linear delay differential equations in a finite dimensional space are Hyers–Ulam stable and hence shadowable. The converse result is available only in the special case of autonomous and periodic linear delay differential equations with a simple spectrum. In this paper, we prove the converse and hence the equivalence of all three notions in the title for a general class of nonautonomous linear delay differential equations with uniformly bounded coefficients. The importance of the boundedness assumption is shown by an example.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Compactified Jacobians of extended ADE curves and Lagrangian fibrations","authors":"Adam Czapliński, Andreas Krug, Manfred Lehn, Sönke Rollenske","doi":"10.1142/s0219199724500044","DOIUrl":"https://doi.org/10.1142/s0219199724500044","url":null,"abstract":"<p>We observe that general reducible curves in sufficiently positive linear systems on K3 surfaces are of a form that generalize Kodaira’s classification of singular elliptic fibers and thus call them extended ADE curves. On such a curve <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>C</mi></math></span><span></span>, we describe a compactified Jacobian and show that its components reflect the intersection graph of <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>C</mi></math></span><span></span>. This extends known results when <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>C</mi></math></span><span></span> is reduced, but new difficulties arise when <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>C</mi></math></span><span></span> is non-reduced. As an application, we get an explicit description of general singular fibers of certain Lagrangian fibrations of Beauville–Mukai type.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140168367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A global Morse index theorem and applications to Jacobi fields on CMC surfaces","authors":"Wu-Hsiung Huang","doi":"10.1142/s0219199723500645","DOIUrl":"https://doi.org/10.1142/s0219199723500645","url":null,"abstract":"<p>In this paper, we establish a “global” Morse index theorem. Given a hypersurface <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span><span></span> of constant mean curvature, immersed in <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℝ</mi></mrow><mrow><mi>n</mi><mo stretchy=\"false\">+</mo><mn>1</mn></mrow></msup></math></span><span></span>. Consider a continuous deformation of “generalized” Lipschitz domain <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>D</mi><mo stretchy=\"false\">(</mo><mi>t</mi><mo stretchy=\"false\">)</mo></math></span><span></span> enlarging in <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span><span></span>. The topological type of <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>D</mi><mo stretchy=\"false\">(</mo><mi>t</mi><mo stretchy=\"false\">)</mo></math></span><span></span> is permitted to change along <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>t</mi></math></span><span></span>, so that <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>D</mi><mo stretchy=\"false\">(</mo><mi>t</mi><mo stretchy=\"false\">)</mo></math></span><span></span> has an arbitrary shape which can “reach afar” in <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span><span></span>, i.e. cover any preassigned area. The proof of the global Morse index theorem is reduced to the continuity in <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><mi>t</mi></math></span><span></span> of the Sobolev space <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>H</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span><span></span> of variation functions on <span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><mi>D</mi><mo stretchy=\"false\">(</mo><mi>t</mi><mo stretchy=\"false\">)</mo></math></span><span></span>, as well as the continuity of eigenvalues of the stability operator. We devise a “detour” strategy by introducing a notion of “set-continuity” of <span><math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"><mi>D</mi><mo stretchy=\"false\">(</mo><mi>t</mi><mo stretchy=\"false\">)</mo></math></span><span></span> in <span><math altimg=\"eq-00013.gif\" display=\"inline\" overflow=\"scroll\"><mi>t</mi></math></span><span></span> to yield the required continuities of <span><math altimg=\"eq-00014.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>H</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span><span></span> and of eigenvalues. The global Morse index theorem thus follows and provides a structural theorem of the existence of Jacobi fields on domains in <span><math altimg=\"eq-00015.gif\" display=\"","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140072483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Concentration phenomena for the fractional relativistic Schrödinger–Choquard equation","authors":"Vincenzo Ambrosio","doi":"10.1142/s021919972350061x","DOIUrl":"https://doi.org/10.1142/s021919972350061x","url":null,"abstract":"<p>We consider the fractional relativistic Schrödinger–Choquard equation <disp-formula-group><span><math altimg=\"eq-00001.gif\" display=\"block\" overflow=\"scroll\"><mrow><mfenced close=\"\" open=\"{\" separators=\"\"><mrow><mtable columnlines=\"none\" equalcolumns=\"false\" equalrows=\"false\"><mtr><mtd columnalign=\"left\"><msup><mrow><mo stretchy=\"false\">(</mo><mo stretchy=\"false\">−</mo><mi mathvariant=\"normal\">Δ</mi><mo stretchy=\"false\">+</mo><msup><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy=\"false\">)</mo></mrow><mrow><mi>s</mi></mrow></msup><mi>u</mi><mo stretchy=\"false\">+</mo><mi>V</mi><mo stretchy=\"false\">(</mo><mi>𝜀</mi><mi>x</mi><mo stretchy=\"false\">)</mo><mi>u</mi><mo>=</mo><mfenced close=\")\" open=\"(\" separators=\"\"><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>μ</mi></mrow></msup></mrow></mfrac><mo stretchy=\"false\">∗</mo><mi>F</mi><mo stretchy=\"false\">(</mo><mi>u</mi><mo stretchy=\"false\">)</mo></mrow></mfenced><mi>f</mi><mo stretchy=\"false\">(</mo><mi>u</mi><mo stretchy=\"false\">)</mo></mtd><mtd columnalign=\"left\"><mstyle><mtext>in</mtext></mstyle><mspace width=\".17em\"></mspace><mspace width=\".17em\"></mspace><msup><mrow><mi>ℝ</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd columnalign=\"left\"><mi>u</mi><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mo stretchy=\"false\">(</mo><msup><mrow><mi>ℝ</mi></mrow><mrow><mi>N</mi></mrow></msup><mo stretchy=\"false\">)</mo><mo>,</mo></mtd><mtd columnalign=\"left\"><mi>u</mi><mo>&gt;</mo><mn>0</mn><mspace width=\".17em\"></mspace><mspace width=\".17em\"></mspace><mstyle><mtext>in</mtext></mstyle><mspace width=\".17em\"></mspace><mspace width=\".17em\"></mspace><msup><mrow><mi>ℝ</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></mrow></math></span><span></span></disp-formula-group> where <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>𝜀</mi><mo>&gt;</mo><mn>0</mn></math></span><span></span> is a small parameter, <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>s</mi><mo>∈</mo><mo stretchy=\"false\">(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo stretchy=\"false\">)</mo></math></span><span></span>, <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>m</mi><mo>&gt;</mo><mn>0</mn></math></span><span></span>, <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>N</mi><mo>&gt;</mo><mn>2</mn><mi>s</mi></math></span><span></span>, <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>μ</mi><mo>∈</mo><mo stretchy=\"false\">(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mi>s</mi><mo stretchy=\"false\">)</mo></math></span><span></span>, <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mo stretchy=\"false\">(</mo><mo stretchy=\"false\">−</mo><mi mathvariant=\"normal\">Δ</mi><mo stretchy=\"false\">+</mo><msup><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy=","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140076158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Toroidal extended affine Lie algebras and vertex algebras","authors":"Fulin Chen, Haisheng Li, Shaobin Tan","doi":"10.1142/s0219199724500032","DOIUrl":"https://doi.org/10.1142/s0219199724500032","url":null,"abstract":"<p>In this paper, we study nullity-<span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mn>2</mn></math></span><span></span> toroidal extended affine Lie algebras in the context of vertex algebras and their <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>ϕ</mi></math></span><span></span>-coordinated modules. Among the main results, we introduce a variant of toroidal extended affine Lie algebras, associate vertex algebras to the variant Lie algebras, and establish a canonical connection between modules for toroidal extended affine Lie algebras and <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>ϕ</mi></math></span><span></span>-coordinated modules for these vertex algebras. Furthermore, by employing some results of Billig, we obtain an explicit realization of a class of irreducible modules for the variant Lie algebras.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140072481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weight module classifications for Bershadsky–Polyakov algebras","authors":"Dražen Adamović, Kazuya Kawasetsu, David Ridout","doi":"10.1142/s0219199723500633","DOIUrl":"https://doi.org/10.1142/s0219199723500633","url":null,"abstract":"<p>The Bershadsky–Polyakov algebras are the subregular quantum Hamiltonian reductions of the affine vertex operator algebras associated with <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>𝔰</mi><mi>𝔩</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span><span></span>. In (D. Adamović, K. Kawasetsu and D. Ridout, A realisation of the Bershadsky–Polyakov algebras and their relaxed modules, <i>Lett. Math. Phys.</i><b>111</b> (2021) 38, arXiv:2007.00396 [math.QA]), we realized these algebras in terms of the regular reduction, Zamolodchikov’s <i>W</i>₃-algebra, and an isotropic lattice vertex operator algebra. We also proved that a natural construction of relaxed highest-weight Bershadsky–Polyakov modules has the property that the result is generically irreducible. Here, we prove that this construction, when combined with spectral flow twists, gives a complete set of irreducible weight modules whose weight spaces are finite-dimensional. This gives a simple independent proof of the main classification theorem of (Z. Fehily, K. Kawasetsu and D. Ridout, Classifying relaxed highest-weight modules for admissible-level Bershadsky–Polyakov algebras, <i>Comm. Math. Phys.</i><b>385</b> (2021) 859–904, arXiv:2007.03917 [math.RT]) for nondegenerate admissible levels and extends this classification to a category of weight modules. We also deduce the classification for the nonadmissible level <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mstyle mathvariant=\"sans-serif\"><mi>k</mi></mstyle><mo>=</mo><mo stretchy=\"false\">−</mo><mfrac><mrow><mn>7</mn></mrow><mrow><mn>3</mn></mrow></mfrac></math></span><span></span>, which is new.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140072484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geodesics on adjoint orbits of SL(n, ℝ)","authors":"Brian Grajales, Lino Grama, Rafaela F. Prado","doi":"10.1142/s0219199724500019","DOIUrl":"https://doi.org/10.1142/s0219199724500019","url":null,"abstract":"<p>In this paper, we examine the geodesics on adjoint orbits of <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">SL</mtext></mstyle><mo stretchy=\"false\">(</mo><mi>n</mi><mo>,</mo><mi>ℝ</mi><mo stretchy=\"false\">)</mo></math></span><span></span> that are equipped with <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">SO</mtext></mstyle><mo stretchy=\"false\">(</mo><mi>n</mi><mo stretchy=\"false\">)</mo></math></span><span></span>-invariant metrics, where <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">SO</mtext></mstyle><mo stretchy=\"false\">(</mo><mi>n</mi><mo stretchy=\"false\">)</mo></math></span><span></span> is the maximal compact subgroup. Our primary technique involves translating this problem into a geometric problem in the tangent bundle of certain <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">SO</mtext></mstyle><mo stretchy=\"false\">(</mo><mi>n</mi><mo stretchy=\"false\">)</mo></math></span><span></span>-flag manifolds and describing the geodesic equations with respect to the Sasaki metric on the tangent bundle. Additionally, we utilize tools from Lie Theory to obtain explicit descriptions of families of geodesics. We provide a detailed analysis of the case for <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">SL</mtext></mstyle><mo stretchy=\"false\">(</mo><mn>2</mn><mo>,</mo><mi>ℝ</mi><mo stretchy=\"false\">)</mo></math></span><span></span>.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140072624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}