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

作　　者：朱业成[1] 

机构地区：[1]安徽工业大学应用数学系,安徽马鞍山243002

出　　处：《数学杂志》2014年第3期432-440,共9页Journal of Mathematics

基　　金：Supported by Youth Talents Key Foundation of Colleges and Universities ofAnhui Province(2012SQRL038ZD);Youth Foundation of AHUT(QZ200918)

摘　　要：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].

关 键 词：超切曲率 法曲率 第二变分公式 紧致性 

分 类 号：O186.16[理学—数学]