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Journal of Geometry and Physics最新文献

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Geometric meaning of momentum conservation
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-11-29 DOI: 10.1016/j.geomphys.2024.105388
Hyungjin Huh
{"title":"Geometric meaning of momentum conservation","authors":"Hyungjin Huh","doi":"10.1016/j.geomphys.2024.105388","DOIUrl":"10.1016/j.geomphys.2024.105388","url":null,"abstract":"<div><div>We define an area function <span><math><mi>A</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span> for Schrödinger equation. The conservation of the area <span><math><mi>A</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>A</mi><mo>(</mo><mn>0</mn><mo>)</mo></math></span> is shown by considering momentum conservation. The similar idea is applied to Dirac equations.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"209 ","pages":"Article 105388"},"PeriodicalIF":1.6,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Anti-Leibniz algebras: A non-commutative version of mock-Lie algebras
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-11-28 DOI: 10.1016/j.geomphys.2024.105385
Safa Braiek , Taoufik Chtioui , Sami Mabrouk
{"title":"Anti-Leibniz algebras: A non-commutative version of mock-Lie algebras","authors":"Safa Braiek ,&nbsp;Taoufik Chtioui ,&nbsp;Sami Mabrouk","doi":"10.1016/j.geomphys.2024.105385","DOIUrl":"10.1016/j.geomphys.2024.105385","url":null,"abstract":"<div><div>Leibniz algebras are non skew-symmetric generalization of Lie algebras. In this paper we introduce the notion of anti-Leibniz algebras as a “non commutative version” of mock-Lie algebras. Low dimensional classification of such algebras is given. Then we investigate the notion of averaging operators and more general embedding tensors to build some new algebraic structures, namely anti-associative dialgebras, anti-associative trialgebras and anti-Leibniz trialgebras.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"209 ","pages":"Article 105385"},"PeriodicalIF":1.6,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Positive mass and Dirac operators on weighted manifolds and smooth metric measure spaces
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-11-28 DOI: 10.1016/j.geomphys.2024.105386
Michael B. Law, Isaac M. Lopez, Daniel Santiago
{"title":"Positive mass and Dirac operators on weighted manifolds and smooth metric measure spaces","authors":"Michael B. Law,&nbsp;Isaac M. Lopez,&nbsp;Daniel Santiago","doi":"10.1016/j.geomphys.2024.105386","DOIUrl":"10.1016/j.geomphys.2024.105386","url":null,"abstract":"<div><div>We show that the weighted positive mass theorem of Baldauf–Ozuch and Chu–Zhu is equivalent to the usual positive mass theorem under suitable regularity, and can be regarded as a positive mass theorem for smooth metric measure spaces. A stronger weighted positive mass theorem is established, unifying and generalizing their results. We also study Dirac operators on certain warped product manifolds associated to smooth metric measure spaces. Applications of this include, among others, an alternative proof for a special case of our positive mass theorem, eigenvalue bounds for the Dirac operator on closed spin manifolds, and a new way to understand the weighted Dirac operator using warped products.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"209 ","pages":"Article 105386"},"PeriodicalIF":1.6,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Soliton resolution for the generalized complex short pulse equation with the weighted Sobolev initial data 具有加权Sobolev初始数据的广义复短脉冲方程的孤子解析
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-11-28 DOI: 10.1016/j.geomphys.2024.105387
Xianguo Geng , Feiying Yan , Jiao Wei
{"title":"Soliton resolution for the generalized complex short pulse equation with the weighted Sobolev initial data","authors":"Xianguo Geng ,&nbsp;Feiying Yan ,&nbsp;Jiao Wei","doi":"10.1016/j.geomphys.2024.105387","DOIUrl":"10.1016/j.geomphys.2024.105387","url":null,"abstract":"<div><div>In this work, the Cauchy problem for the generalized complex short pulse equation with initial conditions in the weighted Sobolev space <span><math><mi>H</mi><mo>(</mo><mi>R</mi><mo>)</mo></math></span> is studied by using the Riemann-Hilbert method and the <span><math><mover><mrow><mo>∂</mo></mrow><mo>‾</mo></mover></math></span>-steepest descent method. Based on the spectral analysis of the Lax pair, the solution of the Cauchy problem can be expressed as solution of a Riemann-Hilbert problem, which is transformed into a solvable model after a series of deformations. Finally, the long-time asymptotics and soliton resolution of the generalized complex short pulse equation in the soliton region are obtained by resorting to the <span><math><mover><mrow><mo>∂</mo></mrow><mo>‾</mo></mover></math></span>-steepest descent method. The results also indicate that the <em>N</em>-soliton solutions of the generalized complex short pulse equation are asymptotically stable.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"209 ","pages":"Article 105387"},"PeriodicalIF":1.6,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 third coefficient in the TYCZ–expansion of the epsilon function of Kähler–Einstein manifolds 论卡勒-爱因斯坦流形ε函数 TYCZ 展开中的第三个系数
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-11-26 DOI: 10.1016/j.geomphys.2024.105384
Simone Cristofori, Michela Zedda
{"title":"On the third coefficient in the TYCZ–expansion of the epsilon function of Kähler–Einstein manifolds","authors":"Simone Cristofori,&nbsp;Michela Zedda","doi":"10.1016/j.geomphys.2024.105384","DOIUrl":"10.1016/j.geomphys.2024.105384","url":null,"abstract":"<div><div>In this paper we compute the third coefficient arising from the TYCZ-expansion of the <em>ε</em>-function associated to a Kähler-Einstein metric and discuss the consequences of its vanishing.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"209 ","pages":"Article 105384"},"PeriodicalIF":1.6,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142722576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 constraint tensor for null hypersurfaces 空超曲面的约束张量
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-11-22 DOI: 10.1016/j.geomphys.2024.105375
Miguel Manzano, Marc Mars
{"title":"The constraint tensor for null hypersurfaces","authors":"Miguel Manzano,&nbsp;Marc Mars","doi":"10.1016/j.geomphys.2024.105375","DOIUrl":"10.1016/j.geomphys.2024.105375","url":null,"abstract":"<div><div>In this work we provide a definition of the constraint tensor of a null hypersurface data which is completely explicit in the extrinsic geometry of the hypersurface. The definition is fully covariant and applies for any topology of the hypersurface. For data embedded in a spacetime, the constraint tensor coincides with the pull-back of the ambient Ricci tensor. As applications of the results, we find three geometric quantities on any transverse submanifold <em>S</em> of the data with remarkably simple gauge behaviour, and prove that the restriction of the constraint tensor to <em>S</em> takes a very simple form in terms of them. We also obtain an identity that generalizes the standard near horizon equation of isolated horizons to totally geodesic null hypersurfaces with any topology. Finally, we prove that when a null hypersurface has product topology, its extrinsic curvature can be uniquely reconstructed from the constraint tensor plus suitable initial data on a cross-section.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"208 ","pages":"Article 105375"},"PeriodicalIF":1.6,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142721953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Dirac generating operators of split Courant algebroids 分裂库朗梯形的狄拉克生成算子
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-11-22 DOI: 10.1016/j.geomphys.2024.105373
Liqiang Cai , Zhuo Chen , Honglei Lang , Maosong Xiang
{"title":"Dirac generating operators of split Courant algebroids","authors":"Liqiang Cai ,&nbsp;Zhuo Chen ,&nbsp;Honglei Lang ,&nbsp;Maosong Xiang","doi":"10.1016/j.geomphys.2024.105373","DOIUrl":"10.1016/j.geomphys.2024.105373","url":null,"abstract":"<div><div>Given a vector bundle <em>A</em> over a smooth manifold <em>M</em> such that the square root <span><math><mi>L</mi></math></span> of the line bundle <span><math><msup><mrow><mo>∧</mo></mrow><mrow><mi>top</mi></mrow></msup><msup><mrow><mi>A</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>⊗</mo><msup><mrow><mo>∧</mo></mrow><mrow><mi>top</mi></mrow></msup><msup><mrow><mi>T</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mi>M</mi></math></span> exists, the Clifford bundle associated to the standard split pseudo-Euclidean vector bundle <span><math><mo>(</mo><mi>E</mi><mo>=</mo><mi>A</mi><mo>⊕</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>,</mo><mo>〈</mo><mo>⋅</mo><mo>,</mo><mo>⋅</mo><mo>〉</mo><mo>)</mo></math></span> admits a spinor bundle <span><math><msup><mrow><mo>∧</mo></mrow><mrow><mo>•</mo></mrow></msup><mi>A</mi><mo>⊗</mo><mi>L</mi></math></span>, whose section space consists of Berezinian half-densities of the graded manifold <span><math><msup><mrow><mi>A</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>[</mo><mn>1</mn><mo>]</mo></math></span>. Inspired by Kosmann-Schwarzbach's formula of deriving operator of split Courant algebroid (or proto-bialgebroid) structures on <span><math><mi>A</mi><mo>⊕</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>, we give an explicit construction of the associate Dirac generating operator introduced by Alekseev and Xu. We prove that the square of the Dirac generating operator is an invariant of the corresponding split Courant algebroid, and also give an explicit expression of this invariant in terms of modular elements.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"208 ","pages":"Article 105373"},"PeriodicalIF":1.6,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142721793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Construction of Markov partitions for the geodesic flow on compact Riemann surfaces of constant negative curvature 为负曲率恒定的紧凑黎曼曲面上的大地流构建马尔可夫分区
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-11-22 DOI: 10.1016/j.geomphys.2024.105374
Huynh M. Hien
{"title":"Construction of Markov partitions for the geodesic flow on compact Riemann surfaces of constant negative curvature","authors":"Huynh M. Hien","doi":"10.1016/j.geomphys.2024.105374","DOIUrl":"10.1016/j.geomphys.2024.105374","url":null,"abstract":"<div><div>It is well-known that hyperbolic flows admit Markov partitions of arbitrarily small size. However, the constructions of Markov partitions for general hyperbolic flows are quite abstract and not easy to understand. To establish a more detailed understanding of Markov partitions, in this paper we consider the geodesic flow on Riemann surfaces of constant negative curvature. We provide a more complete construction of Markov partitions for this hyperbolic flow with explicit forms of rectangles and local cross sections. The local product structure is also calculated in detail.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"208 ","pages":"Article 105374"},"PeriodicalIF":1.6,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142721954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Abelianization of Lie algebroids and Lie groupoids 李代数和李群的无差别化
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-11-17 DOI: 10.1016/j.geomphys.2024.105372
Shuyu Xiao
{"title":"Abelianization of Lie algebroids and Lie groupoids","authors":"Shuyu Xiao","doi":"10.1016/j.geomphys.2024.105372","DOIUrl":"10.1016/j.geomphys.2024.105372","url":null,"abstract":"<div><div>We investigate the abelianization of a Lie algebroid and provide a necessary and sufficient condition for its existence. We also study the abelianization of groupoids and provide sufficient conditions for its existence in the smooth category and a necessary and sufficient condition for its existence in the diffeological category.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"207 ","pages":"Article 105372"},"PeriodicalIF":1.6,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142704676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Quantum spacetimes from general relativity?
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-11-17 DOI: 10.1016/j.geomphys.2024.105370
Albert Much
{"title":"Quantum spacetimes from general relativity?","authors":"Albert Much","doi":"10.1016/j.geomphys.2024.105370","DOIUrl":"10.1016/j.geomphys.2024.105370","url":null,"abstract":"<div><div>We introduce a non-commutative product for curved spacetimes, that can be regarded as a generalization of the Rieffel (or Moyal-Weyl) product. This product employs the exponential map and a Poisson tensor, and the deformed product maintains associativity under the condition that the Poisson tensor Θ satisfies <span><math><msup><mrow><mi>Θ</mi></mrow><mrow><mi>μ</mi><mi>ν</mi></mrow></msup><msub><mrow><mi>∇</mi></mrow><mrow><mi>ν</mi></mrow></msub><msup><mrow><mi>Θ</mi></mrow><mrow><mi>ρ</mi><mi>σ</mi></mrow></msup><mo>=</mo><mn>0</mn></math></span>, in relation to a Levi-Cevita connection. We proceed to solve the associativity condition for various physical spacetimes, uncovering non-commutative structures with compelling properties.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"209 ","pages":"Article 105370"},"PeriodicalIF":1.6,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
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