Isoparametric Hypersurfaces Induced by Navigation in Lorentz Finsler Geometry

作     者：Ming XU Ju TAN Na XU Ming XU;Ju TAN;Na XU

作者机构：School of Mathematical SciencesCapital Normal UniversityBeijing 100048P.R.China School of Microelectronics and Data ScienceAnhui University of TechnologyMaanshan 243032P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2023年第39卷第8期

页      面：1547-1564页

核心收录：

学科分类：07[理学] 0701[理学-数学] 

基　　金：Supported by Beijing Natural Science Foundation(Grant No.1222003) National Natural Science Foundation of China(Grant Nos.12131012,11821101 and 12001007) Natural Science Foundation of Anhui province(Grant Nos.2008085QA03 and 1908085QA03)。 

主　　题：Finsler metric homothetic vector field isoparametric function isoparametric hypersurface Lorentz Finsler metric Zermelo navigation 

摘      要：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.