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Isoparametric Hypersurfaces Induced by Navigation in Lorentz Finsler Geometry

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Xu Ming 1   Tan Ju 2 *   Xu Na 2  
文摘 Using a navigation process with the datum (F, V), in which F is a Finsler metric and the smooth tangent vector field V satisfies F (-V (x)) > 1 everywhere, a Lorentz Finsler metric F can be induced. Isoparametric functions and isoparametric hypersurfaces with or without involving a smooth measure can be defined for F. When the vector field V in the navigation datum is homothetic, we prove the local correspondences between isoparametric functions and isoparametric hypersurfaces before and after this navigation process. Using these correspondences, we provide some examples of isoparametric functions and isoparametric hypersurfaces on a Funk space of Lorentz Randers type.
来源 Acta Mathematica Sinica. English Series ,2023,39(8):1547-1564 【核心库】
DOI 10.1007/s10114-023-1187-x
关键词 Finsler metric ; homothetic vector field ; isoparametric function ; isoparametric hypersur-face ; Lorentz Finsler metric ; Zermelo navigation
地址

1. School of Mathematical Sciences, Capital Normal University, Beijing, 100048  

2. School of Microelectronics and Data Science, Anhui University of Technology, Maanshan, 243032

语种 英文
文献类型 研究性论文
ISSN 1439-8516
学科 数学
基金 北京市自然科学基金 ;  国家自然科学基金 ;  安徽省自然科学基金
文献收藏号 CSCD:7542001

参考文献 共 30 共2页

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引证文献 2 篇

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