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Differential Geometry and its Applications最新文献

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On conformal transformations preserving the Ricci tensor in Finsler geometry 论芬斯勒几何中保留里奇张量的保角变换
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2023-12-11 DOI: 10.1016/j.difgeo.2023.102090
M.H. Shavakh , B. Bidabad
{"title":"On conformal transformations preserving the Ricci tensor in Finsler geometry","authors":"M.H. Shavakh ,&nbsp;B. Bidabad","doi":"10.1016/j.difgeo.2023.102090","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102090","url":null,"abstract":"<div><p><span><span>Here we obtain a classical integral formula on the conformal change of Finsler metrics. As an application, we obtain significant results depending on the sign of the Ricci scalars, for mean Landsberg surfaces and show there is no conformal transformation between two compact mean Landsberg surfaces, one of a non-positive Ricci scalar and another of a non-negative Ricci scalar, except for the case where both Ricci scalars are identically zero. Conformal transformations preserving the </span>Ricci tensor are known as Liouville transformations. Here we show that a Liouville transformation between two compact mean Landsberg manifolds of isotropic </span><em>S</em>-curvature is homothetic. Moreover, every Liouville transformation between two compact Finsler <em>n</em><span>-manifolds of bounded mean value Cartan tensor is homothetic. These results are an extension of the results of M. Obata and S. T. Yau on Riemannian geometry<span> and give a positive answer to a conjecture on Liouville's theorem.</span></span></p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138577471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Principal bundles with holomorphic connections over a Kähler Calabi-Yau manifold 卡勒卡拉比尤流形上具有全态连接的主束
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2023-12-08 DOI: 10.1016/j.difgeo.2023.102093
Indranil Biswas , Sorin Dumitrescu
{"title":"Principal bundles with holomorphic connections over a Kähler Calabi-Yau manifold","authors":"Indranil Biswas ,&nbsp;Sorin Dumitrescu","doi":"10.1016/j.difgeo.2023.102093","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102093","url":null,"abstract":"<div><p><span>We prove that any holomorphic vector bundle admitting a holomorphic connection, over a compact Kähler Calabi-Yau manifold, also admits a flat holomorphic connection. This addresses a particular case of a question asked by Atiyah and generalizes a result previously obtained in </span><span>[6]</span> for simply connected compact Kähler Calabi-Yau manifolds. We give some applications of it in the framework of Cartan geometries and foliated Cartan geometries on Kähler Calabi-Yau manifolds.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138557706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Chekanov torus and Gelfand–Zeitlin torus in S2 × S2 S2中的Chekanov环和Gelfand-Zeitlin环 × S2
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2023-12-07 DOI: 10.1016/j.difgeo.2023.102091
Yoosik Kim
{"title":"Chekanov torus and Gelfand–Zeitlin torus in S2 × S2","authors":"Yoosik Kim","doi":"10.1016/j.difgeo.2023.102091","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102091","url":null,"abstract":"<div><p>The Chekanov torus is the first known <em>exotic</em><span><span> torus, a monotone Lagrangian torus that is not </span>Hamiltonian<span> isotopic to the standard monotone Lagrangian torus. We explore the relationship between the Chekanov torus in </span></span><span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and a monotone Lagrangian torus that had been constructed before Chekanov's construction <span>[6]</span>. We prove that the monotone Lagrangian torus fiber in a certain Gelfand–Zeitlin system is related to the Chekanov torus in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> by a symplectomorphism.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138501413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quasi-Einstein manifolds admitting a closed conformal vector field 准爱因斯坦流形承认闭合共形矢量场
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2023-11-24 DOI: 10.1016/j.difgeo.2023.102083
J.F. Silva Filho
{"title":"Quasi-Einstein manifolds admitting a closed conformal vector field","authors":"J.F. Silva Filho","doi":"10.1016/j.difgeo.2023.102083","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102083","url":null,"abstract":"<div><p>In this article, we investigate quasi-Einstein manifolds admitting a closed conformal vector field. Initially, we present a rigidity result for quasi-Einstein manifolds with constant scalar curvature and carrying a non-parallel closed conformal vector field. Moreover, we prove that quasi-Einstein manifolds admitting a closed conformal vector field can be conformally changed to constant scalar curvature almost everywhere. Finally, we obtain a characterization for quasi-Einstein manifolds endowed with a non-parallel gradient conformal vector field.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138423659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the geometry of conullity two manifolds 关于凸性双流形的几何
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2023-11-23 DOI: 10.1016/j.difgeo.2023.102081
Jacob Van Hook
{"title":"On the geometry of conullity two manifolds","authors":"Jacob Van Hook","doi":"10.1016/j.difgeo.2023.102081","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102081","url":null,"abstract":"<div><p><span><span><span>We consider complete locally irreducible conullity two Riemannian manifolds with constant </span>scalar curvature along </span>nullity geodesics. There exists a naturally defined open </span>dense subset on which we describe the metric in terms of several functions which are uniquely determined up to isometry. In addition, we show that the fundamental group is either trivial or infinite cyclic.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138414197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Brylinski beta function of a double layer 双层的Brylinski函数
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2023-11-21 DOI: 10.1016/j.difgeo.2023.102078
Pooja Rani , M.K. Vemuri
{"title":"The Brylinski beta function of a double layer","authors":"Pooja Rani ,&nbsp;M.K. Vemuri","doi":"10.1016/j.difgeo.2023.102078","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102078","url":null,"abstract":"<div><p><span>An analogue of Brylinski's knot beta function is defined for a compactly supported (Schwartz) distribution </span><em>T</em> on <em>d</em><span>-dimensional Euclidean space. This is a holomorphic function on a right half-plane. If </span><em>T</em><span><span> is a (uniform) double-layer on a compact smooth hypersurface, then the beta function has an </span>analytic continuation<span><span> to the complex plane as a meromorphic function, and the residues are integrals of invariants of the </span>second fundamental form. The first few residues are computed when </span></span><span><math><mi>d</mi><mo>=</mo><mn>2</mn></math></span> and <span><math><mi>d</mi><mo>=</mo><mn>3</mn></math></span>.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138430311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
S-curvature, E-curvature, and Berwald scalar curvature of Finsler spaces s曲率，e曲率，以及Finsler空间的Berwald标量曲率
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2023-11-21 DOI: 10.1016/j.difgeo.2023.102080
M. Crampin
{"title":"S-curvature, E-curvature, and Berwald scalar curvature of Finsler spaces","authors":"M. Crampin","doi":"10.1016/j.difgeo.2023.102080","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102080","url":null,"abstract":"<div><p>I show that the S-curvature of a Finsler space vanishes if and only if the E-curvature vanishes if and only if the Berwald scalar curvature vanishes; and I extend these results to the case in which these objects are isotropic.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138395293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Torsion-free connections on G-structures g型结构的无扭连接
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2023-11-19 DOI: 10.1016/j.difgeo.2023.102075
Brice Flamencourt
{"title":"Torsion-free connections on G-structures","authors":"Brice Flamencourt","doi":"10.1016/j.difgeo.2023.102075","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102075","url":null,"abstract":"<div><p>We prove that for a Lie group <span><math><msub><mrow><mi>SO</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo><mo>⊂</mo><mi>G</mi><mo>⊂</mo><msub><mrow><mi>GL</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo></math></span>, any <em>G</em>-structure on a smooth manifold can be endowed with a torsion free connection which is locally the Levi-Civita connection of a Riemannian metric in a given conformal class. In this process, we classify the admissible groups.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138095784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Legendre magnetic flows for totally η-umbilic real hypersurfaces in a complex hyperbolic space 复双曲空间中全η-脐带实超曲面的勒让德磁流
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2023-11-19 DOI: 10.1016/j.difgeo.2023.102074
Qingsong Shi , Toshiaki Adachi
{"title":"Legendre magnetic flows for totally η-umbilic real hypersurfaces in a complex hyperbolic space","authors":"Qingsong Shi ,&nbsp;Toshiaki Adachi","doi":"10.1016/j.difgeo.2023.102074","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102074","url":null,"abstract":"<div><p><span><span>We study trajectories for Sasakian magnetic fields on horospheres, on geodesic spheres and on tubes around totally geodesic complex hypersurfaces in a complex </span>hyperbolic space. Considering the </span>subbundle<span><span> formed by unit tangent vectors orthogonal to the </span>characteristic vector field, flows associated with trajectories on this subbundle are smoothly conjugate to each other for each geodesic sphere, and are classified into two and three classes for a horosphere and for each tube, respectively.</span></p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138136107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Vector bundles on real abelian varieties 实阿贝尔变种上的向量束
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2023-11-19 DOI: 10.1016/j.difgeo.2023.102077
Archana S. Morye
{"title":"Vector bundles on real abelian varieties","authors":"Archana S. Morye","doi":"10.1016/j.difgeo.2023.102077","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102077","url":null,"abstract":"<div><p>This paper is about real holomorphic vector bundles<span> on real abelian varieties. The main result of the paper gives several conditions that are necessary and sufficient for the existence of a holomorphic connection on a real holomorphic vector bundle over a real abelian variety. Also proved is an analogue, for real abelian varieties, of a result of Simpson, which gives a criterion for a holomorphic vector bundle to arise by successive extensions of stable vector bundles with vanishing Chern classes.</span></p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138136106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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