The Study Of A Class Of Riemann-Finsler Submanifolds

Finsler geometry is an important branch of differential geometry.Under the initiative of Professor Shiing Shen Chern,Finsler geometry has been made a great progress after 1990s.In recent years,influenced by the study of Riemannian submanifolds,the study of Finsler submanifolds has attracted more and more attentions and becomes a hot topic in Finsler geometry.This paper quotes a natural identity in the literature[11]and considers a special class of(?,?)-manifolds((?),(?))with an(?,?)-metric F=??((?)/(?)),in which (?) is the Riemannian metric,and (?) is a one-form.In this paper,firstly,we give the well-known first volume variational formula of Riemannian submanifolds,and introduce the concept of minimal submanifolds(mean curvature vector is zero).Then we apply the knowledge of theory of submanifolds to perform calculations to obtain the Takahashi theorem for minimal submanifolds in the hyperbolic space.Finally,using the natural identity,we study the condition nonexistence of closed orientable BH-minimal submanifolds and HT-minimal surfaces in certain(?,?)-manifolds.