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Differential Geometry and its Applications最新文献

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Rigidity of closed vacuum static spaces
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-02-01 DOI: 10.1016/j.difgeo.2024.102217
Guangyue Huang, Qi Guo, Bingqing Ma
{"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}
引用次数: 0
Subgradient estimates for the equation Δbu+aulog⁡u+bu=0 on complete noncompact pseudo-Hermitian manifolds
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-02-01 DOI: 10.1016/j.difgeo.2024.102223
Biqiang Zhao
{"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}
引用次数: 0
Deformation rigidity of the double Cayley Grassmannian
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-01-31 DOI: 10.1016/j.difgeo.2024.102219
Shin-young Kim , Kyeong-Dong Park
{"title":"Deformation rigidity of the double Cayley Grassmannian","authors":"Shin-young Kim ,&nbsp;Kyeong-Dong Park","doi":"10.1016/j.difgeo.2024.102219","DOIUrl":"10.1016/j.difgeo.2024.102219","url":null,"abstract":"<div><div>The double Cayley Grassmannian is a unique smooth equivariant completion with Picard number one of the 14-dimensional exceptional complex Lie group <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, and it parametrizes eight-dimensional isotropic subalgebras of the complexified bi-octonions. We show the rigidity of the double Cayley Grassmannian under Kähler deformations. This means that for any smooth projective family of complex manifolds over a connected base of which one fiber is biholomorphic to the double Cayley Grassmannian, all other fibers are biholomorphic to the double Cayley Grassmannian.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"99 ","pages":"Article 102219"},"PeriodicalIF":0.6,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143101467","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
Spacelike foliations on Lorentz manifolds
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-01-31 DOI: 10.1016/j.difgeo.2025.102235
Aldir Brasil , Sharief Deshmukh , Euripedes da Silva , Paulo Sousa
{"title":"Spacelike foliations on Lorentz manifolds","authors":"Aldir Brasil ,&nbsp;Sharief Deshmukh ,&nbsp;Euripedes da Silva ,&nbsp;Paulo Sousa","doi":"10.1016/j.difgeo.2025.102235","DOIUrl":"10.1016/j.difgeo.2025.102235","url":null,"abstract":"<div><div>In this work, we study the geometric properties of spacelike foliations by hypersurfaces on a Lorentz manifold. We investigate conditions for the leaves being stable, totally geodesic or totally umbilical. We consider that <span><math><msup><mrow><mover><mrow><mi>M</mi></mrow><mo>‾</mo></mover></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span> is equipped with a timelike closed conformal vector field <em>ξ</em>. If the foliation has constant mean curvature, we show that the leaves are stable. When the leaves are compact spacelike hypersurfaces we show that, under certain conditions, its are totally umbilic hypersurfaces. In the case of foliations by complete noncompact hypersurfaces, we using a Maximum Principle at infinity to conclude that the foliation is totally geodesic.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"99 ","pages":"Article 102235"},"PeriodicalIF":0.6,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143101468","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
Diameter theorems on Kähler and quaternionic Kähler manifolds under a positive lower curvature bound 正下曲率界下Kähler和四元数Kähler流形的直径定理
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2024-11-29 DOI: 10.1016/j.difgeo.2024.102218
Maria Gordina , Gunhee Cho
{"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":"2024-11-29","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}
引用次数: 0
Integral Ricci curvature bounds for possibly collapsed spaces with Ricci curvature bounded from below 里奇曲率自下而上有界的可能坍缩空间的里奇曲率积分界值
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2024-11-21 DOI: 10.1016/j.difgeo.2024.102214
Michael Smith
{"title":"Integral Ricci curvature bounds for possibly collapsed spaces with Ricci curvature bounded from below","authors":"Michael Smith","doi":"10.1016/j.difgeo.2024.102214","DOIUrl":"10.1016/j.difgeo.2024.102214","url":null,"abstract":"<div><div>Assuming a lower bound on the Ricci curvature of a complete Riemannian manifold, for <span><math><mi>q</mi><mo>&lt;</mo><mn>1</mn><mo>/</mo><mn>2</mn></math></span> we show the existence of bounds on the local <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup></math></span> norm of the Ricci curvature that depend only on the dimension and which improve with volume collapse.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"98 ","pages":"Article 102214"},"PeriodicalIF":0.6,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723027","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
Conformal surface splines 共形表面花键
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2024-11-21 DOI: 10.1016/j.difgeo.2024.102200
Yousuf Soliman , Ulrich Pinkall , Peter Schröder
{"title":"Conformal surface splines","authors":"Yousuf Soliman ,&nbsp;Ulrich Pinkall ,&nbsp;Peter Schröder","doi":"10.1016/j.difgeo.2024.102200","DOIUrl":"10.1016/j.difgeo.2024.102200","url":null,"abstract":"<div><div>We introduce a family of boundary conditions and point constraints for conformal immersions that increase the controllability of surfaces defined as minimizers of conformal variational problems. Our free boundary conditions fix the metric on the boundary, up to a global scale, and admit a discretization compatible with discrete conformal equivalence. We also introduce constraints on the conformal scale factor, enforcing rigidity of the geometry in regions of interest, and describe how in the presence of point constraints the conformal class encodes knot points of the spline that can be directly manipulated. To control the tangent planes, we introduce flux constraints balancing the internal material stresses. The collection of these point constraints provide intuitive controls for exploring a subspace of conformal immersions interpolating a fixed set of points in space. We demonstrate the applicability of our framework to geometric modeling, mathematical visualization, and form finding.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"97 ","pages":"Article 102200"},"PeriodicalIF":0.6,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142706899","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
Logarithmic Cartan geometry on complex manifolds with trivial logarithmic tangent bundle 具有微小对数切线束的复流形上的对数卡坦几何
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2024-11-19 DOI: 10.1016/j.difgeo.2024.102213
Indranil Biswas , Sorin Dumitrescu , Archana S. Morye
{"title":"Logarithmic Cartan geometry on complex manifolds with trivial logarithmic tangent bundle","authors":"Indranil Biswas ,&nbsp;Sorin Dumitrescu ,&nbsp;Archana S. Morye","doi":"10.1016/j.difgeo.2024.102213","DOIUrl":"10.1016/j.difgeo.2024.102213","url":null,"abstract":"<div><div>Let <em>M</em> be a compact complex manifold, and <span><math><mi>D</mi><mspace></mspace><mo>⊂</mo><mspace></mspace><mi>M</mi></math></span> a reduced normal crossing divisor on it, such that the logarithmic tangent bundle <span><math><mi>T</mi><mi>M</mi><mo>(</mo><mo>−</mo><mi>log</mi><mo>⁡</mo><mi>D</mi><mo>)</mo></math></span> is holomorphically trivial. Let <span><math><mi>A</mi></math></span> denote the maximal connected subgroup of the group of all holomorphic automorphisms of <em>M</em> that preserve the divisor <em>D</em>. Take a holomorphic Cartan geometry <span><math><mo>(</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>H</mi></mrow></msub><mo>,</mo><mspace></mspace><mi>Θ</mi><mo>)</mo></math></span> of type <span><math><mo>(</mo><mi>G</mi><mo>,</mo><mspace></mspace><mi>H</mi><mo>)</mo></math></span> on <em>M</em>, where <span><math><mi>H</mi><mspace></mspace><mo>⊂</mo><mspace></mspace><mi>G</mi></math></span> are complex Lie groups. We prove that <span><math><mo>(</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>H</mi></mrow></msub><mo>,</mo><mspace></mspace><mi>Θ</mi><mo>)</mo></math></span> is isomorphic to <span><math><mo>(</mo><msup><mrow><mi>ρ</mi></mrow><mrow><mo>⁎</mo></mrow></msup><msub><mrow><mi>E</mi></mrow><mrow><mi>H</mi></mrow></msub><mo>,</mo><mspace></mspace><msup><mrow><mi>ρ</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mi>Θ</mi><mo>)</mo></math></span> for every <span><math><mi>ρ</mi><mspace></mspace><mo>∈</mo><mspace></mspace><mi>A</mi></math></span> if and only if the principal <em>H</em>–bundle <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>H</mi></mrow></msub></math></span> admits a logarithmic connection Δ singular on <em>D</em> such that Θ is preserved by the connection Δ.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"97 ","pages":"Article 102213"},"PeriodicalIF":0.6,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142706900","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
A characterization of parallel surfaces in Minkowski space via minimal and maximal surfaces 通过最小和最大曲面表征闵科夫斯基空间中的平行曲面
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2024-11-15 DOI: 10.1016/j.difgeo.2024.102204
José Eduardo Núñez Ortiz, Gabriel Ruiz-Hernández
{"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":"2024-11-15","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}
引用次数: 0
A Frobenius integrability theorem for plane fields generated by quasiconformal deformations 准共形变形产生的平面场的弗罗贝尼斯可整性定理
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2024-11-14 DOI: 10.1016/j.difgeo.2024.102202
Slobodan N. Simić
{"title":"A Frobenius integrability theorem for plane fields generated by quasiconformal deformations","authors":"Slobodan N. Simić","doi":"10.1016/j.difgeo.2024.102202","DOIUrl":"10.1016/j.difgeo.2024.102202","url":null,"abstract":"<div><div>We generalize the classical Frobenius integrability theorem to plane fields of class <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>Q</mi></mrow></msup></math></span>, a regularity class introduced by Reimann <span><span>[9]</span></span> for vector fields in Euclidean spaces. Reimann showed that a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>Q</mi></mrow></msup></math></span> vector field is uniquely integrable and its flow is a quasiconformal deformation. We prove that an a.e. involutive <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>Q</mi></mrow></msup></math></span> plane field (defined in a suitable way) in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> is integrable, with integral manifolds of class <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>Q</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"97 ","pages":"Article 102202"},"PeriodicalIF":0.6,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142660249","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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