On equifocal Finsler submanifolds and analytic maps

Extrinsic sphere and totally umbilical submanifolds in Finsler spaces

‎Based on a definition for circle in Finsler space‎, ‎recently proposed by one of the present authors and Z‎. ‎Shen‎, ‎a natural definition of extrinsic sphere in Finsler geometry is given and it is shown that a connected submanifold of a Finsler manifold is totally umbilical and has non-zero parallel mean curvature vector field‎, ‎if and only if its circles coincide with circles of the ambient...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Local Zeta Functions Supported on Analytic Submanifolds and Newton Polyhedra

The local zeta functions (also called Igusa’s zeta functions) over p-adic fields are connected with the number of solutions of congruences and exponential sums mod pm. These zeta functions are defined as integrals over open and compact subsets with respect to the Haar measure. In this paper, we introduce new integrals defined over submanifolds, or more generally, over non-degenerate complete in...

extrinsic sphere and totally umbilical submanifolds in finsler spaces

‎based on a definition for circle in finsler space‎, ‎recently proposed by one of the present authors and z‎. ‎shen‎, ‎a natural definition of extrinsic sphere in finsler geometry is given and it is shown that a connected submanifold of a finsler manifold is totally umbilical and has non-zero parallel mean curvature vector field‎, ‎if and only if its circles coincide with circles of the ambient...

A Splitting Theorem for Equifocal Submanifolds in Simply Connected Compact Symmetric Spaces

A submanifold in a symmetric space is called equifocal if it has a globally flat abelian normal bundle and its focal data is invariant under normal parallel transportation. This is a generalization of the notion of isoparametric submanifolds in Euclidean spaces. To each equifocal submanifold, we can associate a Coxeter group, which is determined by the focal data at one point. In this paper we ...