Differential Geometry and its Applications最新文献

{"title":"Diameter theorems on Kähler and quaternionic Kähler manifolds under a positive lower curvature bound","authors":"Maria Gordina ,&nbsp;Gunhee Cho","doi":"10.1016/j.difgeo.2024.102218","DOIUrl":"10.1016/j.difgeo.2024.102218","url":null,"abstract":"<div><div>We define the orthogonal Bakry-Émery tensor as a generalization of the orthogonal Ricci curvature, and then study diameter theorems on Kähler and quaternionic Kähler manifolds under positivity assumption on the orthogonal Bakry-Émery tensor. Moreover, under such assumptions on the orthogonal Bakry-Émery tensor and the holomorphic or quaternionic sectional curvature on a Kähler manifold or a quaternionic Kähler manifold respectively, the Bonnet-Myers type diameter bounds are sharper than in the Riemannian case.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"98 ","pages":"Article 102218"},"PeriodicalIF":0.6,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142746975","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}

{"title":"Gradient estimates of a nonlinear parabolic equation under integral Bakry-Émery Ricci condition","authors":"Xavier Ramos Olivé ,&nbsp;Shoo Seto","doi":"10.1016/j.difgeo.2024.102222","DOIUrl":"10.1016/j.difgeo.2024.102222","url":null,"abstract":"<div><div>We prove a global gradient estimate to positive solutions of the nonlinear parabolic equation <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>f</mi></mrow></msub><mi>u</mi><mo>+</mo><mi>a</mi><mi>u</mi><mi>ln</mi><mo>⁡</mo><mo>(</mo><mi>u</mi><mo>)</mo><mo>+</mo><mi>b</mi><mi>u</mi></math></span> under an integral Bakry-Émery Ricci condition on compact weighted manifolds. The elliptic version of the equation arises in the study of gradient Ricci solitons and in this paper we consider the parabolic version.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"98 ","pages":"Article 102222"},"PeriodicalIF":0.6,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A global invariant for path structures and second order differential equations","authors":"E. Falbel ,&nbsp;J.M. Veloso","doi":"10.1016/j.difgeo.2024.102224","DOIUrl":"10.1016/j.difgeo.2024.102224","url":null,"abstract":"<div><div>We study a global invariant for path structures which is obtained as a secondary invariant from a Cartan connection on a canonical bundle associated to a path structure. This invariant is computed in examples which are defined in terms of reductions of the path structure. In particular we give a formula for this global invariant for second order differential equations defined on a torus <span><math><msup><mrow><mi>T</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"98 ","pages":"Article 102224"},"PeriodicalIF":0.6,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Ricci flow of discrete surfaces of revolution, and relation to constant Gaussian curvature","authors":"Naoya Suda","doi":"10.1016/j.difgeo.2024.102221","DOIUrl":"10.1016/j.difgeo.2024.102221","url":null,"abstract":"<div><div>Giving explicit parametrizations of discrete constant Gaussian curvature surfaces of revolution that are defined from an integrable systems approach, we study Ricci flow for discrete surfaces, and see how discrete surfaces of revolution have a geometric realization for the Ricci flow that approaches the constant Gaussian curvature surfaces we have parametrized.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"98 ","pages":"Article 102221"},"PeriodicalIF":0.6,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176202","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}

{"title":"Subgradient estimates for the equation Δbu+aulog⁡u+bu=0 on complete noncompact pseudo-Hermitian manifolds","authors":"Biqiang Zhao","doi":"10.1016/j.difgeo.2024.102223","DOIUrl":"10.1016/j.difgeo.2024.102223","url":null,"abstract":"<div><div>Let <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>H</mi><mi>M</mi><mo>,</mo><mi>J</mi><mo>,</mo><mi>θ</mi><mo>)</mo></math></span> be a complete pseudo-Hermitian (2m+1)-manifold. In this paper, we derive the subgradient estimates for the positive solutions of the equation <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>b</mi></mrow></msub><mi>u</mi><mo>+</mo><mi>a</mi><mi>u</mi><mi>log</mi><mo>⁡</mo><mi>u</mi><mo>+</mo><mi>b</mi><mi>u</mi><mo>=</mo><mn>0</mn></math></span> on complete noncompact pseudo-Hermitian manifolds without the commutation condition.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"98 ","pages":"Article 102223"},"PeriodicalIF":0.6,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176183","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}

{"title":"Rigidity of closed vacuum static spaces","authors":"Guangyue Huang,&nbsp;Qi Guo,&nbsp;Bingqing Ma","doi":"10.1016/j.difgeo.2024.102217","DOIUrl":"10.1016/j.difgeo.2024.102217","url":null,"abstract":"<div><div>In this paper, we study the rigidity results of closed vacuum static spaces. By introducing a trace-free three tensor, we provide a necessary condition that such spaces with the dimensional scope <span><math><mn>3</mn><mo>≤</mo><mi>n</mi><mo>≤</mo><mn>5</mn></math></span> must be of Einstein.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"98 ","pages":"Article 102217"},"PeriodicalIF":0.6,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176182","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}

{"title":"The Sasakian statistical structures of constant ϕ-sectional curvature on Sasakian space forms","authors":"Xinlei Wu,&nbsp;Yanyan Sheng,&nbsp;Liang Zhang","doi":"10.1016/j.difgeo.2024.102190","DOIUrl":"10.1016/j.difgeo.2024.102190","url":null,"abstract":"<div><p>In this paper, we investigate the Sasakian statistical structures of constant <em>ϕ</em>-sectional curvature based on Sasakian space forms. We obtain the classification of this kind of Sasakian statistical structures. Our classification results show that the Sasakian statistical structures of constant <em>ϕ</em>-sectional curvature on a Sasakian space form with dimension higher than 3 must be almost-trivial; on a 3-dimensional Sasakian space form, in addition to the almost-trivial Sasakian statistical structure, there exist other Sasakian statistical structures which satisfy the constant <em>ϕ</em>-sectional curvature condition. We also point out that a rigidity result for cosymplectic statistical structures of constant <em>ϕ</em>-sectional curvature on 3-dimensional cosymplectic space forms in <span><span>[11]</span></span> can be improved to the corresponding classification result.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"97 ","pages":"Article 102190"},"PeriodicalIF":0.6,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142173432","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}

{"title":"Covariant Schrödinger operator and L2-vanishing property on Riemannian manifolds","authors":"Ognjen Milatovic","doi":"10.1016/j.difgeo.2024.102191","DOIUrl":"10.1016/j.difgeo.2024.102191","url":null,"abstract":"<div><p>Let <em>M</em> be a complete Riemannian manifold satisfying a weighted Poincaré inequality, and let <span><math><mi>E</mi></math></span> be a Hermitian vector bundle over <em>M</em> equipped with a metric covariant derivative ∇. We consider the operator <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>X</mi><mo>,</mo><mi>V</mi></mrow></msub><mo>=</mo><msup><mrow><mi>∇</mi></mrow><mrow><mi>†</mi></mrow></msup><mi>∇</mi><mo>+</mo><msub><mrow><mi>∇</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>+</mo><mi>V</mi></math></span>, where <span><math><msup><mrow><mi>∇</mi></mrow><mrow><mi>†</mi></mrow></msup></math></span> is the formal adjoint of ∇ with respect to the inner product in the space of square-integrable sections of <span><math><mi>E</mi></math></span>, <em>X</em> is a smooth (real) vector field on <em>M</em>, and <em>V</em> is a fiberwise self-adjoint, smooth section of the endomorphism bundle <span><math><mi>End</mi><mspace></mspace><mi>E</mi></math></span>. We give a sufficient condition for the triviality of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-kernel of <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>X</mi><mo>,</mo><mi>V</mi></mrow></msub></math></span>. As a corollary, putting <span><math><mi>X</mi><mo>≡</mo><mn>0</mn></math></span> and working in the setting of a Clifford module equipped with a Clifford connection ∇, we obtain the triviality of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-kernel of <span><math><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, where <em>D</em> is the Dirac operator corresponding to ∇. In particular, when <span><math><mi>E</mi><mo>=</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>C</mi></mrow><mrow><mi>k</mi></mrow></msubsup><msup><mrow><mi>T</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mi>M</mi></math></span> and <span><math><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> is the Hodge–deRham Laplacian on (complex-valued) <em>k</em>-forms, we recover some recent vanishing results for <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-harmonic (complex-valued) <em>k</em>-forms.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"97 ","pages":"Article 102191"},"PeriodicalIF":0.6,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142228643","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}

{"title":"A characterization of parallel surfaces in Minkowski space via minimal and maximal surfaces","authors":"José Eduardo Núñez Ortiz,&nbsp;Gabriel Ruiz-Hernández","doi":"10.1016/j.difgeo.2024.102204","DOIUrl":"10.1016/j.difgeo.2024.102204","url":null,"abstract":"<div><div>We give a characterization of parallel surfaces in the three dimensional Minkowski space. We consider the following construction on a non degenerate surface <em>M</em>. Given a non degenerate curve in the surface we have the ruled surface orthogonal to <em>M</em> along the curve. We prove that if this orthogonal surface is either maximal or minimal then the curve is a geodesic of <em>M</em>. Moreover such geodesic is either a planar line of curvature of <em>M</em> or it has both constant curvature and constant no zero torsion. A first result says that if <em>M</em> is a surface such that through every point pass two non degenerate geodesics, both with constant curvature and torsion, then the surface is parallel. Our main result says that if <em>M</em> is a surface then through every point pass three non degenerate curves whose associated ruled orthogonal surfaces are either maximal or minimal if and only if <em>M</em> is a parallel surface.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"97 ","pages":"Article 102204"},"PeriodicalIF":0.6,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142660250","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}

{"title":"Classification of conformally flat Moebius isoparametric submanifolds in the Euclidean space","authors":"M.S.R. Antas","doi":"10.1016/j.difgeo.2024.102201","DOIUrl":"10.1016/j.difgeo.2024.102201","url":null,"abstract":"<div><div>The aim of this article is to classify umbilic-free isometric immersions <span><math><mi>f</mi><mo>:</mo><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>→</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span>, <span><math><mi>n</mi><mo>≥</mo><mn>4</mn></math></span>, of a conformally flat manifold which are Moebius isoparametric.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"97 ","pages":"Article 102201"},"PeriodicalIF":0.6,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142660369","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}