Finsler流形中弧长第二变分与子流形(英文)

THE SECOND VARIATION OF ARC-LENGTH AND SUBMANIFOLDS IN FINSLER MANIFOLD

本文研究了Finsler流形中的子流形的相关问题.利用文[23,24]中引入的Finsler流形中的切曲率和法曲率的概念,计算出Finsler流形中测地线的一个新的第二变分公式,获得了关于Finsler子流形中几何不变量和拓扑不变量的一些新的关系,推广了文[4]的许多结果.

In this paper, we study submanifolds in Finsler manifold M. By using tangent curvature and normal curvature, which are introduced in [23, 24], we derive a new second variation formula for a geodesic 7 in Finsler manifold, and then obtain many relation between geometric invariants and topological invariants of Finsler submanifolds, which are generalizations of the results described in [4].