Journal of Geometry and Physics最新文献

{"title":"Generalized Hamilton spaces: New developments and applications","authors":"J.J. Relancio ,&nbsp;L. Santamaría-Sanz","doi":"10.1016/j.geomphys.2025.105626","DOIUrl":"10.1016/j.geomphys.2025.105626","url":null,"abstract":"<div><div>In this work, we present new developments in generic cotangent bundle geometries, depending on all phase-space variables. In particular, we will focus on the so-called generalized Hamilton spaces, discussing how the main ingredients of this geometrical framework, such as the Hamiltonian and the nonlinear and affine connections, can be derived from a given metric. Several properties of this kind of spaces have been demonstrated for autoparallel Hamiltonians. Moreover, we study the spacetime and momentum isometries of the metric. Finally, we discuss the possible applications of cotangent bundle geometries in quantum gravity, such as the construction of deformed relativistic kinematics and non-commutative spacetimes.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105626"},"PeriodicalIF":1.2,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144893527","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 vanishing theorem in K-theory for spectral projections of a non-periodic magnetic Schrödinger operator","authors":"Yuri A. Kordyukov ,&nbsp;Vladimir M. Manuilov","doi":"10.1016/j.geomphys.2025.105625","DOIUrl":"10.1016/j.geomphys.2025.105625","url":null,"abstract":"<div><div>We consider the Schrödinger operator <span><math><mi>H</mi><mo>(</mo><mi>μ</mi><mo>)</mo><mo>=</mo><msubsup><mrow><mi>∇</mi></mrow><mrow><mi>A</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><msub><mrow><mi>∇</mi></mrow><mrow><mi>A</mi></mrow></msub><mo>+</mo><mi>μ</mi><mi>V</mi></math></span> on a Riemannian manifold <em>M</em> of bounded geometry, where <span><math><mi>μ</mi><mo>&gt;</mo><mn>0</mn></math></span> is a coupling parameter, the magnetic field <span><math><mi>B</mi><mo>=</mo><mi>d</mi><mi>A</mi></math></span> and the electric potential <em>V</em> are uniformly <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>-bounded, <span><math><mi>V</mi><mo>≥</mo><mn>0</mn></math></span>. We assume that, for some <span><math><msub><mrow><mi>E</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>0</mn></math></span>, each connected component of the sublevel set <span><math><mo>{</mo><mi>V</mi><mo>&lt;</mo><msub><mrow><mi>E</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>}</mo></math></span> of the potential <em>V</em> is relatively compact. Under some assumptions on geometric and spectral properties of the connected components, we show that, for sufficiently large <em>μ</em>, the spectrum of <span><math><mi>H</mi><mo>(</mo><mi>μ</mi><mo>)</mo></math></span> in the interval <span><math><mo>[</mo><mn>0</mn><mo>,</mo><msub><mrow><mi>E</mi></mrow><mrow><mn>0</mn></mrow></msub><mi>μ</mi><mo>]</mo></math></span> has a gap, the spectral projection of <span><math><mi>H</mi><mo>(</mo><mi>μ</mi><mo>)</mo></math></span>, corresponding to the interval <span><math><mo>(</mo><mo>−</mo><mo>∞</mo><mo>,</mo><mi>λ</mi><mo>]</mo></math></span> with <em>λ</em> in the gap, belongs to the Roe <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>M</mi><mo>)</mo></math></span> of the manifold <em>M</em>, and, if <em>M</em> is not compact, its class in the <em>K</em> theory of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>M</mi><mo>)</mo></math></span> is trivial.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105625"},"PeriodicalIF":1.2,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144904413","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":"Interpreting the Ooguri-Vafa symplectic form à la Atiyah-Bott","authors":"Danny Nackan","doi":"10.1016/j.geomphys.2025.105624","DOIUrl":"10.1016/j.geomphys.2025.105624","url":null,"abstract":"<div><div>Gaiotto, Moore, and Neitzke predicted that the hyperkähler Ooguri-Vafa space <span><math><msup><mrow><mi>M</mi></mrow><mrow><mi>ov</mi></mrow></msup></math></span> should provide a local model for Hitchin moduli spaces near the discriminant locus. To this end, Tulli identified <span><math><msup><mrow><mi>M</mi></mrow><mrow><mi>ov</mi></mrow></msup></math></span> with a certain space of framed Higgs bundles with an irregular singularity. We extend this result by identifying the Ooguri-Vafa holomorphic symplectic form with a regularized version of the Atiyah-Bott form on the associated space of framed connections. We also prove the analogous statement for the corresponding semiflat forms. Finally, restricting to the Hitchin section, we identify a regularized version of Hitchin's <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-metric with the Ooguri-Vafa metric.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105624"},"PeriodicalIF":1.2,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144893526","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":"Corrigendum to “Local and 2-local automorphisms of some solvable Leibniz algebras”","authors":"F.N. Arzikulov ,&nbsp;I.A. Karimjanov ,&nbsp;S.M. Umrzaqov","doi":"10.1016/j.geomphys.2025.105623","DOIUrl":"10.1016/j.geomphys.2025.105623","url":null,"abstract":"<div><div>In the present paper, we provide a corrected version of the incorrect Theorem 4.3 from the paper “Local and 2-local automorphisms of some solvable Leibniz algebras” by F.N. Arzikulov, I.A. Karimjanov, and S.M. Umrzaqov (2022) <span><span>[2]</span></span> and completely prove Theorem 4.4.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105623"},"PeriodicalIF":1.2,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144861010","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":"Concave symplectic toric fillings","authors":"Aleksandra Marinković","doi":"10.1016/j.geomphys.2025.105622","DOIUrl":"10.1016/j.geomphys.2025.105622","url":null,"abstract":"<div><div>As shown by Etnyre and Honda (<span><span>[2]</span></span>), every contact 3-manifold admits infinitely many concave symplectic fillings that are mutually not symplectomorphic and not related by blow ups. In this note we refine this result in the toric setting by showing that every contact toric 3-manifold admits infinitely many concave symplectic toric fillings that are mutually not equivariantly symplectomorphic and not related by blow ups. The concave symplectic toric structure is constructed on certain linear and cyclic plumbings over spheres.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105622"},"PeriodicalIF":1.2,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144861011","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":"Complete complex Finsler metrics and uniform equivalence of the Kobayashi metric","authors":"Jun Nie","doi":"10.1016/j.geomphys.2025.105621","DOIUrl":"10.1016/j.geomphys.2025.105621","url":null,"abstract":"<div><div>In this paper, first of all, according to Lu's and Zhang's works about the curvature of the Bergman metric on a bounded domain and the properties of the squeezing functions, we observe that Bergman curvatures of the Bergman metric on a bounded strictly pseudoconvex domain with <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-boundary or bounded convex domain are bounded. Applying to the Schwarz lemma from a complete Kähler manifold into a complex Finsler manifold, we get that a bounded strictly pseudoconvex domain with <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-boundary or bounded convex domain admits complete strongly pseudoconvex complex Finsler metrics such that their holomorphic sectional curvature is bounded from above by a negative constant. Finally, by the Schwarz lemma from a complete Kähler manifold into a complex Finsler manifold, we prove the uniform equivalences of the Kobayashi metric and Carathéodory metric on a bounded strongly convex domain with smooth boundary.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105621"},"PeriodicalIF":1.2,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144828552","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":"Solitonic geometry of Magneto fluid spacetimes: Ricci Bourguignon insights and energy momentum characterizations","authors":"Karthika Ramasamy,&nbsp;Soumendu Roy","doi":"10.1016/j.geomphys.2025.105609","DOIUrl":"10.1016/j.geomphys.2025.105609","url":null,"abstract":"<div><div>The main objective of our current article is to inspect the solitonic aspect of relativistic magneto-fluid spacetime if its metric is Ricci Bourguignon soliton. We explored some geometrical behaviour of magneto-fluid spacetime emerged with a Ricci Bourguignon soliton. We accomplished a few characterizations of magneto-fluid spacetime in relation to a Ricci bourguignon soliton with a <span><math><mi>ϕ</mi><mo>(</mo><mi>Q</mi><mo>)</mo></math></span>-vector field, torse-forming vector field and conformal Killing vector field. Also, we determine the con-harmonically flat, <span><math><msub><mrow><mi>W</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-flat and <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-flat curvature state of a magneto-fluid spacetime admitting Ricci bourguignon soliton. Eventually, we explored the magneto-fluid spacetime model characterized by a specific form of energy-momentum tensor in which the pressure equals the energy density. Also, we explicit an example to verify our result. Furthermore, this investigation may offer new insights into the magneto-geometric behaviour of compact astrophysical objects such as neutron stars and magnetars, and opens unexplored avenues for geometric modelling in magnetohydrodynamic engineering and modified gravity theories.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105609"},"PeriodicalIF":1.2,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144828553","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":"Variation formulas and Jiang's theorem for f-biharmonic maps on Riemannian foliations","authors":"Xueshan Fu ,&nbsp;Jinhua Qian ,&nbsp;Seoung Dal Jung","doi":"10.1016/j.geomphys.2025.105604","DOIUrl":"10.1016/j.geomphys.2025.105604","url":null,"abstract":"<div><div>On foliations, there are two kinds of harmonic maps, that is, transversally harmonic map and <span><math><mo>(</mo><mi>F</mi><mo>,</mo><msup><mrow><mi>F</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></math></span>-harmonic map between Riemannian foliations <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>F</mi><mo>)</mo></math></span> and <span><math><mo>(</mo><msup><mrow><mi>M</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>,</mo><msup><mrow><mi>g</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>,</mo><msup><mrow><mi>F</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></math></span>. These are extended to another (bi)harmonic maps. In this paper, we study several harmonic and biharmonic maps on foliations. In particular, we give the variation formulas and prove the Jiang's theorem for transversally <em>f</em>-biharmonic map, transversally bi-<em>f</em>-harmonic map, <span><math><msub><mrow><mo>(</mo><mi>F</mi><mo>,</mo><msup><mrow><mi>F</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></mrow><mrow><mi>f</mi></mrow></msub></math></span>-biharmonic map and bi-<span><math><msub><mrow><mo>(</mo><mi>F</mi><mo>,</mo><msup><mrow><mi>F</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></mrow><mrow><mi>f</mi></mrow></msub></math></span>-harmonic maps on foliations, where <em>f</em> is a positive basic function.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105604"},"PeriodicalIF":1.2,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144766597","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":"Surfaces of three-dimensional homogeneous plane waves","authors":"Giovanni Calvaruso,&nbsp;Lorenzo Pellegrino","doi":"10.1016/j.geomphys.2025.105603","DOIUrl":"10.1016/j.geomphys.2025.105603","url":null,"abstract":"<div><div>We investigate the geometry of surfaces in three-dimensional homogeneous non-symmetric plane waves. In particular, we obtain the full classification and explicit description of their totally geodesic and parallel examples and prove the nonexistence of proper totally umbilical surfaces. Moreover, we characterize their minimal surfaces, providing some explicit examples.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105603"},"PeriodicalIF":1.2,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144738584","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":"Kähler toric manifolds from dually flat spaces","authors":"Mathieu Molitor","doi":"10.1016/j.geomphys.2025.105602","DOIUrl":"10.1016/j.geomphys.2025.105602","url":null,"abstract":"<div><div>We present a novel geometric construction, called <em>torification</em>, that associates Kähler manifolds with torus actions to dually flat manifolds. The construction relies on information-theoretical concepts and aims to provide clear directions for developing Geometric Quantum Mechanics further in finite dimension.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105602"},"PeriodicalIF":1.2,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144738583","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}