Isoparametric Hypersurfaces Induced by Navigation in Lorentz Finsler Geometry  

作　　者：Ming XU Ju TAN Na XU 

机构地区：[1]School of Mathematical Sciences,Capital Normal University,Beijing 100048,P.R.China [2]School of Microelectronics and Data Science,Anhui University of Technology,Maanshan 243032,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第8期1547-1564,共18页数学学报（英文版）

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)。

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.

关 键 词：Finsler metric homothetic vector field isoparametric function isoparametric hypersurface Lorentz Finsler metric Zermelo navigation 

分 类 号：O186.1[理学—数学]