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Pseudo-Conformal actions of the Möbius group Möbius基团的伪共形作用
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2023-10-11 DOI: 10.1016/j.difgeo.2023.102070
M. Belraouti , M. Deffaf , Y. Raffed , A. Zeghib
{"title":"Pseudo-Conformal actions of the Möbius group","authors":"M. Belraouti ,&nbsp;M. Deffaf ,&nbsp;Y. Raffed ,&nbsp;A. Zeghib","doi":"10.1016/j.difgeo.2023.102070","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102070","url":null,"abstract":"<div><p>We study compact connected pseudo-Riemannian manifolds <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> on which the conformal group <span><math><mi>Conf</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> acts essentially and transitively. We prove, in particular, that if the non-compact semi-simple part of <span><math><mi>Conf</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> is the Möbius group, then <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> is conformally flat.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49758929","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: 1
Geometry and topology of manifolds with integral radial curvature bounds 具有积分径向曲率边界的流形的几何和拓扑
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2023-10-06 DOI: 10.1016/j.difgeo.2023.102064
Jing Mao
{"title":"Geometry and topology of manifolds with integral radial curvature bounds","authors":"Jing Mao","doi":"10.1016/j.difgeo.2023.102064","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102064","url":null,"abstract":"<div><p>In this paper, we systematically investigate the geometry and topology of manifolds with integral <em>radial</em> curvature bounds, and obtain many interesting and important conclusions.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49749636","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: 4
Time analyticity for the parabolic type Schrödinger equation on Riemannian manifold with integral Ricci curvature condition 具有积分Ricci曲率条件的黎曼流形上抛物型Schrödinger方程的时间分析性
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2023-10-01 DOI: 10.1016/j.difgeo.2023.102045
Wen Wang
{"title":"Time analyticity for the parabolic type Schrödinger equation on Riemannian manifold with integral Ricci curvature condition","authors":"Wen Wang","doi":"10.1016/j.difgeo.2023.102045","DOIUrl":"10.1016/j.difgeo.2023.102045","url":null,"abstract":"<div><p>In the paper, we investigate the pointwise time analyticity of the parabolic type Schrödinger equation on a complete Riemannian manifold with integral Ricci curvature condition.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47156979","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
Geometry of cascade feedback linearizable control systems 串级反馈线性控制系统的几何特性
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2023-10-01 DOI: 10.1016/j.difgeo.2023.102044
Taylor J. Klotz
{"title":"Geometry of cascade feedback linearizable control systems","authors":"Taylor J. Klotz","doi":"10.1016/j.difgeo.2023.102044","DOIUrl":"10.1016/j.difgeo.2023.102044","url":null,"abstract":"<div><p>Cascade feedback linearization provides geometric insights on explicit integrability of nonlinear control systems with symmetry. A central piece of the theory requires that the partial contact curve reduction of the contact sub-connection be static feedback linearizable. This work establishes new necessary conditions on the equations of Lie type - in the abelian case - that arise in a contact sub-connection with the desired static feedback linearizability property via families of codimension one partial contact curves. Furthermore, an explicit class of contact sub-connections admitting static feedback linearizable contact curve reductions is presented, hinting at a possible classification of all such contact sub-connections. Key tools in proving, and stating, the main results of this paper are truncated versions of the total derivative and Euler operators. Additionally, the Battilotti-Califano system with three inputs is used as a clarifying example of both cascade feedback linearization and the new necessary conditions.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42535409","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: 1
Implicit contact dynamics and Hamilton-Jacobi theory 隐式接触动力学与Hamilton-Jacobi理论
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2023-10-01 DOI: 10.1016/j.difgeo.2023.102030
Oğul Esen , Manuel Lainz Valcázar , Manuel de León , Cristina Sardón
{"title":"Implicit contact dynamics and Hamilton-Jacobi theory","authors":"Oğul Esen ,&nbsp;Manuel Lainz Valcázar ,&nbsp;Manuel de León ,&nbsp;Cristina Sardón","doi":"10.1016/j.difgeo.2023.102030","DOIUrl":"10.1016/j.difgeo.2023.102030","url":null,"abstract":"<div><p>In this paper, we introduce implicit Hamiltonian dynamics in the framework of contact geometry in two different ways: first, we introduce classical implicit Hamiltonian dynamics on a contact manifold, followed by evolution Hamiltonian dynamics. In the first case, implicit contact Hamiltonian dynamics is defined as a Legendrian submanifold of a tangent contact space, whilst the implicit evolution dynamic is understood as a Lagrangian submanifold of a certain symplectic space embedded into the tangent contact space. To conclude, we propose a geometric Hamilton-Jacobi theory for both of these formulations.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49523002","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: 5
Riemannian exponential and quantization 黎曼指数与量子化
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2023-10-01 DOI: 10.1016/j.difgeo.2023.102047
J. Muñoz-Díaz, R.J. Alonso-Blanco
{"title":"Riemannian exponential and quantization","authors":"J. Muñoz-Díaz,&nbsp;R.J. Alonso-Blanco","doi":"10.1016/j.difgeo.2023.102047","DOIUrl":"10.1016/j.difgeo.2023.102047","url":null,"abstract":"<div><p>This article continues and completes the previous one <span>[18]</span>. First of all, we present two methods of quantization associated with a linear connection given on a differentiable manifold, one of them being the one presented in <span>[18]</span>. The two methods allow quantization of functions that come from covariant tensor fields. The equivalence of both is demonstrated as a consequence of a remarkable property of the Riemannian exponential (<span>Theorem 5.1</span>) that, as far as we know, is new to the literature. In addition, we provide a characterization of the Schrödinger operators as the only ones that by quantization correspond to classical mechanical systems. Finally, it is shown that the extension of the above quantization to functions of a very broad type can be carried out by generalizing the method of <span>[18]</span> in terms of fields of distributions.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42593781","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 rigidity of the Sasakian structure and characterization of cosymplectic manifolds 关于Sasakian结构的刚性与协辛流形的表征
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2023-10-01 DOI: 10.1016/j.difgeo.2023.102043
Dhriti Sundar Patra , Vladimir Rovenski
{"title":"On the rigidity of the Sasakian structure and characterization of cosymplectic manifolds","authors":"Dhriti Sundar Patra ,&nbsp;Vladimir Rovenski","doi":"10.1016/j.difgeo.2023.102043","DOIUrl":"10.1016/j.difgeo.2023.102043","url":null,"abstract":"<div><p>We introduce new metric structures on a smooth manifold (called “weak” structures) that generalize the almost contact, Sasakian, cosymplectic, etc. metric structures <span><math><mo>(</mo><mi>φ</mi><mo>,</mo><mi>ξ</mi><mo>,</mo><mi>η</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> and allow us to take a fresh look at the classical theory and find new applications. This assertion is illustrated by generalizing several well-known results. It is proved that any Sasakian structure is rigid, i.e., our weak Sasakian structure is homothetically equivalent to a Sasakian structure. It is shown that a weak almost contact structure with parallel tensor <em>φ</em> is a weak cosymplectic structure and an example of such a structure on the product of manifolds is given. Conditions are found under which a vector field is a weak contact vector field.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43180268","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: 7
The Atiyah class of generalized holomorphic vector bundles 广义全纯向量丛的Atiyah类
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2023-10-01 DOI: 10.1016/j.difgeo.2023.102031
Honglei Lang , Xiao Jia , Zhangju Liu
{"title":"The Atiyah class of generalized holomorphic vector bundles","authors":"Honglei Lang ,&nbsp;Xiao Jia ,&nbsp;Zhangju Liu","doi":"10.1016/j.difgeo.2023.102031","DOIUrl":"10.1016/j.difgeo.2023.102031","url":null,"abstract":"<div><p>We introduce the notion of Atiyah class of a generalized holomorphic vector bundle, which captures the obstruction to the existence of generalized holomorphic connections on the bundle. As in the classical holomorphic case, this Atiyah class can be defined in three different ways: using Čech cohomology, using the first-jet short exact sequence, or adopting the Lie pair point of view.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43561464","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 estimates for submanifolds in manifolds with nonnegative curvature 非负曲率流形中子流形的直径估计
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2023-10-01 DOI: 10.1016/j.difgeo.2023.102048
Jia-Yong Wu
{"title":"Diameter estimates for submanifolds in manifolds with nonnegative curvature","authors":"Jia-Yong Wu","doi":"10.1016/j.difgeo.2023.102048","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102048","url":null,"abstract":"<div><p>Given a closed connected manifold smoothly immersed in a complete noncompact Riemannian manifold with nonnegative sectional curvature, we estimate the intrinsic diameter of the submanifold in terms of its mean curvature field integral. On the other hand, for a compact convex surface with boundary smoothly immersed in a complete noncompact Riemannian manifold with nonnegative sectional curvature, we can estimate its intrinsic diameter in terms of its mean curvature field integral and the length of its boundary. These results are supplements of previous work of Topping, Wu-Zheng and Paeng.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49759444","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
Relative connections on principal bundles and relative equivariant structures 主丛上的相对连接与相对等变结构
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2023-10-01 DOI: 10.1016/j.difgeo.2023.102041
Mainak Poddar , Anoop Singh
{"title":"Relative connections on principal bundles and relative equivariant structures","authors":"Mainak Poddar ,&nbsp;Anoop Singh","doi":"10.1016/j.difgeo.2023.102041","DOIUrl":"10.1016/j.difgeo.2023.102041","url":null,"abstract":"<div><p>We investigate relative holomorphic connections on a principal bundle over a family of compact complex manifolds. A sufficient condition is given for the existence of a relative holomorphic connection on a holomorphic principal bundle over a complex analytic family. We also introduce the notion of relative equivariant bundles and establish its relation with relative holomorphic connections on principal bundles.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47551262","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: 14
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