{"title":"Legendre magnetic flows for totally η-umbilic real hypersurfaces in a complex hyperbolic space","authors":"Qingsong Shi , Toshiaki Adachi","doi":"10.1016/j.difgeo.2023.102074","DOIUrl":null,"url":null,"abstract":"<div><p><span><span>We study trajectories for Sasakian magnetic fields on horospheres, on geodesic spheres and on tubes around totally geodesic complex hypersurfaces in a complex </span>hyperbolic space. Considering the </span>subbundle<span><span> formed by unit tangent vectors orthogonal to the </span>characteristic vector field, flows associated with trajectories on this subbundle are smoothly conjugate to each other for each geodesic sphere, and are classified into two and three classes for a horosphere and for each tube, respectively.</span></p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"91 ","pages":"Article 102074"},"PeriodicalIF":0.6000,"publicationDate":"2023-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Geometry and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0926224523001006","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We study trajectories for Sasakian magnetic fields on horospheres, on geodesic spheres and on tubes around totally geodesic complex hypersurfaces in a complex hyperbolic space. Considering the subbundle formed by unit tangent vectors orthogonal to the characteristic vector field, flows associated with trajectories on this subbundle are smoothly conjugate to each other for each geodesic sphere, and are classified into two and three classes for a horosphere and for each tube, respectively.
期刊介绍：
Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.
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