Journal of Geometry and Physics最新文献

{"title":"On the maximal superintegrability of strongly isochronous Hamiltonians","authors":"L. Fehér","doi":"10.1016/j.geomphys.2024.105409","DOIUrl":"10.1016/j.geomphys.2024.105409","url":null,"abstract":"<div><div>We study strongly isochronous Hamiltonians that generate periodic time evolution with the same basic period for a dense set of initial values. We explain that all such Hamiltonians are maximally superintegrable, and show that if the system is subjected to Hamiltonian reduction based on a compact symmetry group and certain conditions are met, then the reduced Hamiltonian is strongly isochronous with the original basic period. We utilize these simple observations for demonstrating the maximal superintegrability of rational spin Calogero–Moser type models in confining harmonic potential.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"209 ","pages":"Article 105409"},"PeriodicalIF":1.6,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Novikov Poisson bialgebra","authors":"Bei Li,&nbsp;Dingguo Wang","doi":"10.1016/j.geomphys.2024.105403","DOIUrl":"10.1016/j.geomphys.2024.105403","url":null,"abstract":"<div><div>In this paper, we present the concept of Novikov Poisson bialgebra and establish the equivalence between matched pairs, Manin triples, and Novikov Poisson bialgebras. Specifically, a Novikov Poisson bialgebra can be derived by uniformly solving the associative Yang-Baxter equation and the Novikov Yang-Baxter equation. Furthermore, we introduce the concepts of <span><math><mi>O</mi></math></span>-operators on Novikov Poisson algebras and pre-Novikov Poisson algebras.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"209 ","pages":"Article 105403"},"PeriodicalIF":1.6,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143092367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The exponentially harmonic heat flow on Riemannian manifolds and gradient estimates","authors":"Yan Wang","doi":"10.1016/j.geomphys.2024.105405","DOIUrl":"10.1016/j.geomphys.2024.105405","url":null,"abstract":"<div><div>Suppose that <em>M</em> is a complete Riemannian manifolds with nonnegative sectional curvature. We prove that for the exponentially harmonic heat flow <span><span>(3)</span></span> on bounded regular domain with the Dirichlet initial-boundary value data, there exists a unique global solution. We prove that for any bounded solution of the exponentially harmonic function heat flow on <em>M</em>, there is a gradient estimate. As a consequence of this estimate, we derive the Liouville type theorem for bounded ancient solutions to exponentially harmonic function heat flow on <em>M</em>. We also obtain Liouville type results for the exponentially harmonic functions with finite weighted <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norms.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"209 ","pages":"Article 105405"},"PeriodicalIF":1.6,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143105223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A coadjoint orbit–like construction for Jordan superalgebras","authors":"Florio M. Ciaglia ,&nbsp;Shuhan Jiang ,&nbsp;Jürgen Jost ,&nbsp;Lorenz Schwachhöfer","doi":"10.1016/j.geomphys.2024.105404","DOIUrl":"10.1016/j.geomphys.2024.105404","url":null,"abstract":"<div><div>We investigate the canonical pseudo-Riemannian metrics on the Jordan-analogues of the coadjoint superorbits of a unital pseudo-Euclidean Jordan superalgebra with a positive even part.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"209 ","pages":"Article 105404"},"PeriodicalIF":1.6,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143105222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Zindler curves in non-Euclidean geometry","authors":"David Rochera","doi":"10.1016/j.geomphys.2024.105402","DOIUrl":"10.1016/j.geomphys.2024.105402","url":null,"abstract":"<div><div>In this paper Zindler curves are studied in elliptic and hyperbolic planes. In some cases, these curves are associated to self-parallel curves through a double-traced closed curve with an odd number of singularities via front tire-track curves and parallel curves. It is shown that similar properties to those of planar Zindler curves are satisfied as well. Moreover, easy explicit parameterizations of these curves can be given through Leichtweiss support functions and some examples are constructed.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"209 ","pages":"Article 105402"},"PeriodicalIF":1.6,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Toda Darboux transformations and vacuum expectation values","authors":"Chengwei Wang ,&nbsp;Mengyao Chen ,&nbsp;Jipeng Cheng","doi":"10.1016/j.geomphys.2024.105399","DOIUrl":"10.1016/j.geomphys.2024.105399","url":null,"abstract":"<div><div>The determinant formulas for the vacuum expectation values <span><math><mo>〈</mo><mi>s</mi><mo>+</mo><mi>k</mi><mo>+</mo><mi>n</mi><mo>−</mo><mi>m</mi><mo>,</mo><mo>−</mo><mi>s</mi><mo>|</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>H</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></msup><msubsup><mrow><mi>β</mi></mrow><mrow><mi>m</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>⋯</mo><msubsup><mrow><mi>β</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>⁎</mo></mrow></msubsup><msub><mrow><mi>β</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>⋯</mo><msub><mrow><mi>β</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>g</mi><mo>|</mo><mi>k</mi><mo>〉</mo></math></span> are obtained through the application of Toda Darboux transformations. Initially, it is noted that the 2–Toda hierarchy can be regarded as the 2–component bosonization of the fermionic KP hierarchy. Subsequently, two fundamental Toda Darboux transformation operators, namely <span><math><msub><mrow><mi>T</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>(</mo><mi>q</mi><mo>)</mo><mo>=</mo><mi>Λ</mi><mo>(</mo><mi>q</mi><mo>)</mo><mo>⋅</mo><mi>Δ</mi><mo>⋅</mo><msup><mrow><mi>q</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span> and <span><math><msub><mrow><mi>T</mi></mrow><mrow><mo>−</mo></mrow></msub><mo>(</mo><mi>r</mi><mo>)</mo><mo>=</mo><msup><mrow><mi>Λ</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><msup><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>⋅</mo><msup><mrow><mi>Δ</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>⋅</mo><mi>r</mi></math></span>, are constructed from the changes in the Toda (adjoint) wave functions, by employing the 2–component boson–fermion correspondence. On this basis, the aforementioned vacuum expectation values can be realized as the multi–step Toda Darboux transformations. Therefore, the corresponding determinant formulas are derived from the determinant representations of these Toda Darboux transformations. Ultimately, by adopting similar methodologies, we also present the determinant formulas for <span><math><mo>〈</mo><mi>n</mi><mo>−</mo><mi>m</mi><mo>|</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>H</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></msup><msubsup><mrow><mi>β</mi></mrow><mrow><mi>m</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>⋯</mo><msubsup><mrow><mi>β</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>⁎</mo></mrow></msubsup><msub><mrow><mi>β</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>⋯</mo><msub><mrow><mi>β</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>g</mi><mo>|</mo><mi>k</mi><mo>〉</mo></math></span>, which are associated with the KP tau functions.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"209 ","pages":"Article 105399"},"PeriodicalIF":1.6,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On conormal Lie algebras of Feigin–Odesskii Poisson structures","authors":"Leonid Gorodetsky ,&nbsp;Nikita Markarian","doi":"10.1016/j.geomphys.2024.105400","DOIUrl":"10.1016/j.geomphys.2024.105400","url":null,"abstract":"<div><div>The main result of the paper is a description of conormal Lie algebras of Feigin–Odesskii Poisson structures. In order to obtain it, we introduce a new variant of a definition of a Feigin–Odesskii Poisson structure: we define it using a differential on the second page of a certain spectral sequence. In the general case, this spectral sequence computes morphisms and higher <span><math><msup><mrow><mi>Ext</mi></mrow><mrow><mo>′</mo></mrow></msup><mspace></mspace><mi>s</mi></math></span> between filtered objects in an Abelian category. Moreover, we use our definition to give another proof of the description of symplectic leaves of Feigin–Odesskii Poisson structures.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"209 ","pages":"Article 105400"},"PeriodicalIF":1.6,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143095978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Minimal Lagrangian surfaces in CP2 via the loop group method part II: The general case","authors":"Josef F. Dorfmeister ,&nbsp;Hui Ma","doi":"10.1016/j.geomphys.2024.105398","DOIUrl":"10.1016/j.geomphys.2024.105398","url":null,"abstract":"<div><div>We extend the techniques introduced in <span><span>[10]</span></span> for contractible Riemann surfaces to construct minimal Lagrangian immersions from arbitrary Riemann surfaces into the complex projective plane <span><math><mi>C</mi><msup><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> via the loop group method. Based on the potentials of translationally equivariant minimal Lagrangian surfaces, we introduce perturbed equivariant minimal Lagrangian surfaces in <span><math><mi>C</mi><msup><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and construct a class of minimal Lagrangian cylinders. Furthermore, we show that these minimal Lagrangian cylinders approximate Delaunay cylinders with respect to some weighted Wiener norm of the twisted loop group <span><math><mi>Λ</mi><mi>S</mi><mi>U</mi><msub><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mrow><mi>σ</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"209 ","pages":"Article 105398"},"PeriodicalIF":1.6,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lagrangian H-umbilical submanifolds in complex space forms and pseudo-parallel cubic form","authors":"Huiyang Xu ,&nbsp;Cece Li ,&nbsp;Cheng Xing","doi":"10.1016/j.geomphys.2024.105401","DOIUrl":"10.1016/j.geomphys.2024.105401","url":null,"abstract":"<div><div>Lagrangian <em>H</em>-umbilical submanifolds in complex space forms, as the “simplest” Lagrangian submanifolds next to the geodesic ones, were introduced and determined by B.-Y. Chen. Many interesting examples belong to this class, such as the Whitney spheres, isotropic non-minimal immersions, and special Calabi product immersions. In this paper, such submanifolds are proved to be of a conformally flat, quasi-Einstein metric and the pseudo-parallel cubic form. As the main results, we find a geometric characterization of those submanifolds as not being of constant sectional curvature. Meanwhile, for Lagrangian submanifolds in complex space forms with pseudo-parallel cubic form, we completely determine the three dimensional case, and all dimensions for the conformally flat case.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"209 ","pages":"Article 105401"},"PeriodicalIF":1.6,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stable tree expressions with Omega-classes and double ramification cycles","authors":"Xavier Blot ,&nbsp;Danilo Lewański ,&nbsp;Paolo Rossi ,&nbsp;Sergei Shadrin","doi":"10.1016/j.geomphys.2024.105391","DOIUrl":"10.1016/j.geomphys.2024.105391","url":null,"abstract":"<div><div>We propose a new system of conjectural relations in the tautological ring of the moduli space of curves involving stable rooted trees with level structure decorated by Hodge and Ω-classes and prove these conjectures in different cases.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"209 ","pages":"Article 105391"},"PeriodicalIF":1.6,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}