Classifications of Isoparametric Hypersurfaces in Randers Space Forms  

作　　者：Qun HE Pei Long DONG Song Ting YIN 

机构地区：[1]School of Mathematical Sciences,Tongji University,Shanghai 200092,P.R.China [2]Department of Mathematics and Computer Science,Tongling University,Tongling 244000,P.R.China [3]Key Laboratory of Applied Mathematics(Putian University),Fujian Province University

出　　处：《Acta Mathematica Sinica,English Series》2020年第9期1049-1060,共12页数学学报（英文版）

基　　金：Supported by NNSFC(Grant Nos.11471246 and 11971253);AHNSF(Grant No.1608085MA03);KLAMFJPU(Grant No.SX201805);The authors would like to thank the referees for their time and valuable comments.

摘　　要：In this paper,we give the complete classifications of isoparametric hypersurfaces in Randers space forms.By studying the principal curvatures of anisotropic submanifolds in a Randers space(N,F)with the navigation data(h,W),we find that a Randers space form(N,F,dμBH)and the corresponding Riemannian space(N,h)have the same isoparametric hypersurfaces,but in general,their isoparametric functions are different.We give a necessary and sufficient condition for an isoparametric function of(N,h)to be isoparametric on(N,F,dμBH),from which we get some examples of isoparametric functions.

关 键 词：Isoparametric HYPERSURFACE Randers space FORM principal CURVATURE ANISOTROPIC sub-manifold 

分 类 号：O186.11[理学—数学]