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...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.展开更多
基金Supported by NNSFC(Grant Nos.11471246 and 11971253)AHNSF(Grant No.1608085MA03)+1 种基金KLAMFJPU(Grant No.SX201805)The authors would like to thank the referees for their time and valuable comments.
文摘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.
