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Differential Geometry and its Applications最新文献

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Banach Poisson–Lie groups, Lax equations and the AKS theorem in infinite dimensions 无限维中的Banach泊松-李群，Lax方程和AKS定理
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-12-01 Epub Date: 2025-11-18 DOI: 10.1016/j.difgeo.2025.102310
Tomasz Goliński , Alice Barbora Tumpach
{"title":"Banach Poisson–Lie groups, Lax equations and the AKS theorem in infinite dimensions","authors":"Tomasz Goliński ,&nbsp;Alice Barbora Tumpach","doi":"10.1016/j.difgeo.2025.102310","DOIUrl":"10.1016/j.difgeo.2025.102310","url":null,"abstract":"<div><div>In this paper, we investigate the theory of <em>R</em>-brackets, Baxter brackets and Nijenhuis brackets in the Banach setting, in particular in relation with Banach Poisson–Lie groups. The notion of Banach Lie–Poisson space with respect to an arbitrary duality pairing is crucial for the equations of motion to make sense. In the presence of a non-degenerate invariant pairing on a Banach Lie algebra, these equations of motion assume a Lax form. We prove a version of the Adler–Kostant–Symes theorem adapted to <em>R</em>-matrices on infinite-dimensional Banach algebras. Applications to the resolution of Lax equations associated to some Banach Manin triples are given. The semi-infinite Toda lattice is also presented as an example of this approach.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102310"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145579251","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 note on the Lorentzian splitting theorem 关于洛伦兹分裂定理的注解
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-12-01 Epub Date: 2025-10-06 DOI: 10.1016/j.difgeo.2025.102301
Gregory J. Galloway
{"title":"A note on the Lorentzian splitting theorem","authors":"Gregory J. Galloway","doi":"10.1016/j.difgeo.2025.102301","DOIUrl":"10.1016/j.difgeo.2025.102301","url":null,"abstract":"<div><div>We present a version of the Lorentzian splitting theorem under a weakened Ricci curvature condition. The proof makes use of basic properties of achronal limits <span><span>[19]</span></span>, <span><span>[20]</span></span>, together with the geometric maximum principle for <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> spacelike hypersurfaces in <span><span>[1]</span></span>. Our version strengthens a related result in <span><span>[29]</span></span> in the globally hyperbolic setting by removing a certain boundedness condition on the Ricci curvature.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102301"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266332","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 note on pullbacks and blowups of Lie algebroids, singular foliations, and Dirac structures 李代数、奇叶和狄拉克结构的回调和膨胀注解
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-12-01 Epub Date: 2025-09-18 DOI: 10.1016/j.difgeo.2025.102296
Andreas Schüßler, Marco Zambon
{"title":"A note on pullbacks and blowups of Lie algebroids, singular foliations, and Dirac structures","authors":"Andreas Schüßler,&nbsp;Marco Zambon","doi":"10.1016/j.difgeo.2025.102296","DOIUrl":"10.1016/j.difgeo.2025.102296","url":null,"abstract":"<div><div>Lie algebroids, singular foliations, and Dirac structures are closely related objects. We examine the relation between their pullbacks under maps satisfying a constant rank or transversality assumption. A special case is given by blowdown maps. In that case, we also establish the relation between the blowup of a Lie algebroid and its singular foliation.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102296"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106184","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
Stability of non-diagonal Einstein metrics on homogeneous spaces H × H/ΔK 齐次空间H × H/ΔK上非对角爱因斯坦度量的稳定性
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-12-01 Epub Date: 2025-09-22 DOI: 10.1016/j.difgeo.2025.102295
Valeria Gutiérrez
{"title":"Stability of non-diagonal Einstein metrics on homogeneous spaces H × H/ΔK","authors":"Valeria Gutiérrez","doi":"10.1016/j.difgeo.2025.102295","DOIUrl":"10.1016/j.difgeo.2025.102295","url":null,"abstract":"<div><div>We consider the homogeneous space <span><math><mi>M</mi><mo>=</mo><mi>H</mi><mo>×</mo><mi>H</mi><mo>/</mo><mi>Δ</mi><mi>K</mi></math></span>, where <span><math><mi>H</mi><mo>/</mo><mi>K</mi></math></span> is an irreducible symmetric space and Δ<em>K</em> denotes diagonal embedding. Recently, Lauret and Will provided a complete classification of <span><math><mi>H</mi><mo>×</mo><mi>H</mi></math></span>-invariant Einstein metrics on M. They obtained that there is always at least one non-diagonal Einstein metric on <em>M</em>, and in some cases, diagonal Einstein metrics also exist. We give a formula for the scalar curvature of a subset of <span><math><mi>H</mi><mo>×</mo><mi>H</mi></math></span>-invariant metrics and study the stability of non-diagonal Einstein metrics on <em>M</em> with respect to the Hilbert action, obtaining that these metrics are unstable with different coindices for all homogeneous spaces <em>M</em>.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102295"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145109231","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 CAT(κ) surfaces 在CAT（κ）表面上
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-12-01 Epub Date: 2025-11-07 DOI: 10.1016/j.difgeo.2025.102307
Saajid Chowdhury , Hechen Hu , Matthew Romney , Adam Tsou
{"title":"On CAT(κ) surfaces","authors":"Saajid Chowdhury ,&nbsp;Hechen Hu ,&nbsp;Matthew Romney ,&nbsp;Adam Tsou","doi":"10.1016/j.difgeo.2025.102307","DOIUrl":"10.1016/j.difgeo.2025.102307","url":null,"abstract":"<div><div>We study the properties of <span><math><mi>CAT</mi><mo>(</mo><mi>κ</mi><mo>)</mo></math></span> surfaces: length metric spaces homeomorphic to a surface having curvature bounded above in the sense of satisfying the <span><math><mi>CAT</mi><mo>(</mo><mi>κ</mi><mo>)</mo></math></span> condition locally. The main facts about <span><math><mi>CAT</mi><mo>(</mo><mi>κ</mi><mo>)</mo></math></span> surfaces seem to be largely a part of mathematical folklore, and this paper is intended to rectify the situation. We provide a complete proof that <span><math><mi>CAT</mi><mo>(</mo><mi>κ</mi><mo>)</mo></math></span> surfaces have bounded (integral) curvature. This fact allows one to apply the established theory of surfaces of bounded curvature to derive further properties of <span><math><mi>CAT</mi><mo>(</mo><mi>κ</mi><mo>)</mo></math></span> surfaces. We also show that <span><math><mi>CAT</mi><mo>(</mo><mi>κ</mi><mo>)</mo></math></span> surfaces can be approximated by smooth Riemannian surfaces of Gaussian curvature at most <em>κ</em>. We do this by giving explicit formulas for smoothing the vertices of model polyhedral surfaces.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102307"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145465771","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
Minimal hypersurfaces in S5 with constant scalar curvature and zero Gauss curvature 具有常标量曲率和零高斯曲率的S5极小超曲面
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-12-01 Epub Date: 2025-09-09 DOI: 10.1016/j.difgeo.2025.102279
Qing Cui
{"title":"Minimal hypersurfaces in S5 with constant scalar curvature and zero Gauss curvature","authors":"Qing Cui","doi":"10.1016/j.difgeo.2025.102279","DOIUrl":"10.1016/j.difgeo.2025.102279","url":null,"abstract":"<div><div>We show that a closed minimal hypersurface in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>5</mn></mrow></msup></math></span> with constant scalar curvature and zero Gauss curvature is totally geodesic, which gives a support to strong version of Chern conjecture.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102279"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020439","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 real projective blowup of Poisson structures 泊松结构的实投影爆破
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-12-01 Epub Date: 2025-09-19 DOI: 10.1016/j.difgeo.2025.102293
Andreas Schüßler
{"title":"On the real projective blowup of Poisson structures","authors":"Andreas Schüßler","doi":"10.1016/j.difgeo.2025.102293","DOIUrl":"10.1016/j.difgeo.2025.102293","url":null,"abstract":"<div><div>We give a proof in the context of smooth differential geometry of Polishchuk's theorem from 1997, in which he established under which conditions, given a Poisson scheme <em>M</em> and a Poisson subscheme <em>N</em>, the Poisson structure lifts to the blowup of <em>M</em> along <em>N</em>.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102293"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106320","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
Hodge decomposition of the Sobolev space H1 on a space form of nonpositive curvature 非正曲率空间形式上Sobolev空间H1的Hodge分解
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-12-01 Epub Date: 2025-11-17 DOI: 10.1016/j.difgeo.2025.102311
Chi Hin Chan , Magdalena Czubak , Carlos Pinilla Suarez
{"title":"Hodge decomposition of the Sobolev space H1 on a space form of nonpositive curvature","authors":"Chi Hin Chan ,&nbsp;Magdalena Czubak ,&nbsp;Carlos Pinilla Suarez","doi":"10.1016/j.difgeo.2025.102311","DOIUrl":"10.1016/j.difgeo.2025.102311","url":null,"abstract":"<div><div>The Hodge decomposition is well-known for compact manifolds. The result has been extended by Kodaira to include non-compact manifolds and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> forms. We further extend the Hodge decomposition to the Sobolev space <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> for general <em>k</em>-forms on non-compact manifolds of nonpositive constant sectional curvature. As a result, we also obtain a decomposition on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102311"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145579252","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 hemi-slant submersion from Sasakian manifold sasaki歧管的保形半倾斜浸没
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-01 Epub Date: 2025-06-05 DOI: 10.1016/j.difgeo.2025.102263
Tanveer Fatima , Mohammad Shuaib
{"title":"Conformal hemi-slant submersion from Sasakian manifold","authors":"Tanveer Fatima ,&nbsp;Mohammad Shuaib","doi":"10.1016/j.difgeo.2025.102263","DOIUrl":"10.1016/j.difgeo.2025.102263","url":null,"abstract":"<div><div>In this article, we examine conformal hemi-slant submersion from Sasakian manifold onto a Riemannian manifold which generalizes the conformal anti-invariant, conformal semi-invariant and conformal slant submersions and non-trivial examples are provided. We have also covered integrability requirements and address the necessary and sufficient conditions for the totally geodesicness of distributions. Moreover, the sufficient condition for a conformal hemi-slant submersion to be a homothetic map is investigated. The condition for a total manifold of the submersion to be twisted product is also studied, followed by other decomposition theorems.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"100 ","pages":"Article 102263"},"PeriodicalIF":0.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222617","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 geometry of line-symmetric rigid-body motions 线对称刚体运动的几何学
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-01 Epub Date: 2025-07-15 DOI: 10.1016/j.difgeo.2025.102270
D. Bayril , J.M. Selig
{"title":"The geometry of line-symmetric rigid-body motions","authors":"D. Bayril ,&nbsp;J.M. Selig","doi":"10.1016/j.difgeo.2025.102270","DOIUrl":"10.1016/j.difgeo.2025.102270","url":null,"abstract":"<div><div>In this work the kinematic geometry of line-symmetric rigid-body motions is revisited. These motions are produced by reflecting a rigid body in the successive generator lines of a ruled surface. Classical results are re-derived using methods from Lie algebra and new results are found. In particular, results for some of the acceleration properties of these motions are found using the Sannia frame of the ruled surfaces. The ruled surfaces considered are given by the tangent, normal or binormal lines to smooth curves as well as Catalan surfaces and right conoids.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"100 ","pages":"Article 102270"},"PeriodicalIF":0.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144631355","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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