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Topology of toric gravitational instantons 环状引力瞬子拓扑学
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2024-07-31 DOI: 10.1016/j.difgeo.2024.102171
Gustav Nilsson
{"title":"Topology of toric gravitational instantons","authors":"Gustav Nilsson","doi":"10.1016/j.difgeo.2024.102171","DOIUrl":"10.1016/j.difgeo.2024.102171","url":null,"abstract":"<div><p>For an asymptotically locally Euclidean (ALE) or asymptotically locally flat (ALF) gravitational instanton <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> with toric symmetry, we express the signature of <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> directly in terms of its rod structure. Applying Hitchin–Thorpe-type inequalities for Ricci-flat ALE/ALF manifolds, we formulate, as a step toward a classification of toric ALE/ALF instantons, necessary conditions that the rod structures of such spaces must satisfy. Finally, we apply these results to the study of rod structures with three turning points.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"96 ","pages":"Article 102171"},"PeriodicalIF":0.6,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0926224524000640/pdfft?md5=1af94bc08a68f11151c59c10b99043ce&pid=1-s2.0-S0926224524000640-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141961512","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}
引用次数: 0
Schwarz lemma for conformal parametrization of minimal graphs in M×R M×R 中最小图共形参数化的 Schwarz Lemma
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2024-06-26 DOI: 10.1016/j.difgeo.2024.102169
David Kalaj
{"title":"Schwarz lemma for conformal parametrization of minimal graphs in M×R","authors":"David Kalaj","doi":"10.1016/j.difgeo.2024.102169","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102169","url":null,"abstract":"<div><p>We prove Schwarz-type lemma results for Weierstrass parameterization of the minimal disk in the Riemannian manifold <span><math><mi>M</mi><mo>×</mo><mi>R</mi></math></span>, where <em>M</em> is a Riemannian surface of non-positive Gaussian curvature. The estimate is sharp, and the equality is attained if and only if the <em>ϱ</em>-harmonic mapping that produces the parameterization is conformal and the metric is a Euclidean metric. If the area of the minimal surface is equal to the area of the disk, then the parametrization is a contraction w.r.t. induced metric and hyperbolic metric respectively.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"96 ","pages":"Article 102169"},"PeriodicalIF":0.6,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141481516","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
Equivariant harmonic maps of the complex projective spaces into the quaternion projective spaces 复投影空间到四元投影空间的等调和映射
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2024-06-26 DOI: 10.1016/j.difgeo.2024.102167
Isami Koga , Yasuyuki Nagatomo
{"title":"Equivariant harmonic maps of the complex projective spaces into the quaternion projective spaces","authors":"Isami Koga ,&nbsp;Yasuyuki Nagatomo","doi":"10.1016/j.difgeo.2024.102167","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102167","url":null,"abstract":"<div><p>We classify equivariant harmonic maps of the complex projective spaces <span><math><mi>C</mi><msup><mrow><mi>P</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span> into the quaternion projective spaces. To do this, we employ differential geometry of vector bundles and connections. When the domain is the complex projective <em>line</em>, we have one parameter family of those maps. (This result is already shown in <span>[2]</span> and <span>[4]</span> in other ways). However, when <span><math><mi>m</mi><mo>≧</mo><mn>2</mn></math></span>, we will obtain the rigidity results.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"96 ","pages":"Article 102167"},"PeriodicalIF":0.6,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0926224524000603/pdfft?md5=50c3b21df49c5a546924763a29df2d65&pid=1-s2.0-S0926224524000603-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141481519","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}
引用次数: 0
The curvature tensors associated with the gluing formula of the zeta-determinants for the Robin boundary condition 与罗宾边界条件的zeta决定因子胶合公式相关的曲率张量
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2024-06-25 DOI: 10.1016/j.difgeo.2024.102165
Klaus Kirsten , Yoonweon Lee
{"title":"The curvature tensors associated with the gluing formula of the zeta-determinants for the Robin boundary condition","authors":"Klaus Kirsten ,&nbsp;Yoonweon Lee","doi":"10.1016/j.difgeo.2024.102165","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102165","url":null,"abstract":"<div><p>The gluing formula for the zeta-determinants of Laplacians with respect to the Robin boundary condition was proved in <span>[15]</span>. This formula contains a constant which is expressed by some curvature tensors on the cutting hypersurface including the scalar and principal curvatures. In this paper we compute this constant explicitly when the cutting hypersurface is a 2-dimensional closed submanifold in a closed Riemannian manifold, and discuss some related topics. We next use the conformal rescaling of the Riemannian metric to compute the value of the zeta function at zero associated to the generalized Dirichlet-to-Neumann operator defined by the Robin boundary condition on this cutting hypersurface.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"96 ","pages":"Article 102165"},"PeriodicalIF":0.6,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141481517","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
Hua operators on homogeneous line bundles over non-tube type bounded symmetric domains 非管型有界对称域上同质线束上的华算子
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2024-06-21 DOI: 10.1016/j.difgeo.2024.102168
Fouzia El Wassouli, Daoud Oukacha
{"title":"Hua operators on homogeneous line bundles over non-tube type bounded symmetric domains","authors":"Fouzia El Wassouli,&nbsp;Daoud Oukacha","doi":"10.1016/j.difgeo.2024.102168","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102168","url":null,"abstract":"<div><p>Let <span><math><mi>Ω</mi><mo>=</mo><mi>G</mi><mo>/</mo><mi>K</mi></math></span> be a bounded symmetric domain of non-compact type. In this paper the image of the Poisson transform on the degenerate principal series representations of <em>G</em> attached to the Shilov boundary of Ω is considered. We characterize the images in terms of the third-order Hua operators <span><math><msub><mrow><mi>U</mi></mrow><mrow><mi>ν</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>ν</mi></mrow></msub></math></span>. When Ω is the exceptional domain of type <em>V</em>, we give the explicit formulas for the operators <span><math><msub><mrow><mi>U</mi></mrow><mrow><mi>ν</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>ν</mi></mrow></msub></math></span>.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"96 ","pages":"Article 102168"},"PeriodicalIF":0.6,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141438667","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
Sasakian geometry on sphere bundles II: Constant scalar curvature 球面束上的萨萨基几何 II：恒定标量曲率
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2024-06-20 DOI: 10.1016/j.difgeo.2024.102166
Charles P. Boyer , Christina W. Tønnesen-Friedman
{"title":"Sasakian geometry on sphere bundles II: Constant scalar curvature","authors":"Charles P. Boyer ,&nbsp;Christina W. Tønnesen-Friedman","doi":"10.1016/j.difgeo.2024.102166","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102166","url":null,"abstract":"<div><p>In a previous paper <span>[18]</span> the authors employed the fiber join construction of Yamazaki <span>[38]</span> together with the admissible construction of Apostolov, Calderbank, Gauduchon, and Tønnesen-Friedman <span>[2]</span> to construct new extremal Sasaki metrics on odd dimensional sphere bundles over smooth projective algebraic varieties. In the present paper we continue this study by applying a recent existence theorem <span>[14]</span> that shows that under certain conditions one can always obtain a constant scalar curvature Sasaki metric in the Sasaki cone. Moreover, we explicitly describe this construction for certain sphere bundles of dimension 5 and 7.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"96 ","pages":"Article 102166"},"PeriodicalIF":0.6,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141434496","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
Rotationally invariant translators of the mean curvature flow in Einstein's static universe 爱因斯坦静态宇宙中平均曲率流的旋转不变平移器
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2024-05-30 DOI: 10.1016/j.difgeo.2024.102153
Miguel Ortega , Handan Yıldırım
{"title":"Rotationally invariant translators of the mean curvature flow in Einstein's static universe","authors":"Miguel Ortega ,&nbsp;Handan Yıldırım","doi":"10.1016/j.difgeo.2024.102153","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102153","url":null,"abstract":"<div><p>In this paper, we deal with non-degenerate translators of the mean curvature flow in the well-known Einstein's static universe. We focus on the rotationally invariant translators, that is, those invariant by a natural isometric action of the special orthogonal group on the ambient space. In the classification list, there are three space-like cases and five time-like cases. All of them, except a totally geodesic example, have one or two conic singularities. Also, we show a uniqueness result based on the behaviour of the translator on its boundary. As an application, we extend an isometry of the sphere to the whole translator under simple conditions. This leads to a characterization of a bowl-like example.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"95 ","pages":"Article 102153"},"PeriodicalIF":0.5,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0926224524000469/pdfft?md5=6bc58615dc3e4e9f74770ce03c1820e6&pid=1-s2.0-S0926224524000469-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141244155","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}
引用次数: 0
Isoparametric hypersurfaces in product spaces of space forms 空间形式乘积空间中的等参数超曲面
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2024-05-28 DOI: 10.1016/j.difgeo.2024.102155
Dong Gao , Hui Ma , Zeke Yao
{"title":"Isoparametric hypersurfaces in product spaces of space forms","authors":"Dong Gao ,&nbsp;Hui Ma ,&nbsp;Zeke Yao","doi":"10.1016/j.difgeo.2024.102155","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102155","url":null,"abstract":"<div><p>We give a complete classification of isoparametric hypersurfaces in a product space <span><math><msubsup><mrow><mi>M</mi></mrow><mrow><msub><mrow><mi>κ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><mn>2</mn></mrow></msubsup><mo>×</mo><msubsup><mrow><mi>M</mi></mrow><mrow><msub><mrow><mi>κ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mrow><mn>2</mn></mrow></msubsup></math></span> of 2-dimensional space forms for <span><math><msub><mrow><mi>κ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>∈</mo><mo>{</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></span> with <span><math><msub><mrow><mi>κ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≠</mo><msub><mrow><mi>κ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. In fact we prove that any isoparametric hypersurface in such a space has constant product angle function, which enables us to remove the condition of constant principal curvatures from the classification obtained recently by J.B.M. dos Santos and J.P. dos Santos.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"95 ","pages":"Article 102155"},"PeriodicalIF":0.5,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141244156","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
Absolutely continuous curves in Finsler-like spaces 类芬斯勒空间中的绝对连续曲线
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2024-05-23 DOI: 10.1016/j.difgeo.2024.102154
Fue Zhang , Wei Zhao
{"title":"Absolutely continuous curves in Finsler-like spaces","authors":"Fue Zhang ,&nbsp;Wei Zhao","doi":"10.1016/j.difgeo.2024.102154","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102154","url":null,"abstract":"<div><p>The present paper is devoted to the investigation of absolutely continuous curves in asymmetric metric spaces induced by Finsler structures. Firstly, for asymmetric spaces induced by Finsler manifolds, we show that three different kinds of absolutely continuous curves coincide when their domains are bounded closed intervals. As an application, a universal existence and regularity theorem for gradient flow is obtained in the Finsler setting. Secondly, we study absolutely continuous curves in Wasserstein spaces over Finsler manifolds and establish the Lisini structure theorem in this setting, which characterize the nature of absolutely continuous curves in Wasserstein spaces in terms of dynamical transference plans concentrated on absolutely continuous curves in base Finsler manifolds. Besides, a close relation between continuity equations and absolutely continuous curves in Wasserstein spaces is founded. Last but not least, we also consider nonsmooth “Finsler-like” spaces, in which case most of the aforementioned results remain valid. Various model examples are constructed in this paper, which point out genuine differences between the asymmetric and symmetric settings.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"96 ","pages":"Article 102154"},"PeriodicalIF":0.5,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141084325","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
Almost-Kähler four-manifolds with harmonic self-dual Weyl curvature 具有谐波自双韦尔曲率的近凯勒四面体
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2024-04-30 DOI: 10.1016/j.difgeo.2024.102141
Inyoung Kim
{"title":"Almost-Kähler four-manifolds with harmonic self-dual Weyl curvature","authors":"Inyoung Kim","doi":"10.1016/j.difgeo.2024.102141","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102141","url":null,"abstract":"<div><p>We show that a compact almost-Kähler four-manifold <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>ω</mi><mo>)</mo></math></span> with harmonic self-dual Weyl curvature and constant scalar curvature is Kähler if <span><math><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>⋅</mo><mo>[</mo><mi>ω</mi><mo>]</mo><mo>≥</mo><mn>0</mn></math></span>. We also prove an integral curvature inequality for compact almost-Kähler four-manifolds with harmonic self-dual Weyl curvature.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"94 ","pages":"Article 102141"},"PeriodicalIF":0.5,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140813458","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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