Finsler子流形的若干结果  

Some results on finsler submanifolds

作　　者：吴炳烨[1] 

机构地区：[1]闽江学院数学系,福建福州350108

出　　处：《闽江学院学报》2007年第2期1-5,共5页Journal of Minjiang University

基　　金：福建省教育厅科技项目(S0650024);闽江学院科研项目(YKQ05002)

摘　　要：研究Finsler子流形的若干性质.首先给出了Finsler流形能等距浸入到高维Minkowski空间中的一个新的简单的必要条件,即任何能等距浸入到Minkowski空间中的Finsler流形必定具有有限一致常数.其次以子流形的法曲率、T-曲率以及一致常数研究其象半径,当外围Finsler流形的旗曲率有上界时,得到了象半径估计,它是Riemannian几何中相关结果在Finsler几何中的推广.Some properties for Finsler submanifolds are studied. A new and simple necessary condition for a Finsler manifold can be isometrically immersed into high dimensional Minkowski space is given, namely, any Finsler manifold that can be isometrically immersed into Minkowski space must have finite uniformity constant. The image radius of Finsler submanifolds is also discussed by means of normal curvature, T-curvature and uniformity constant. When the flag curvature of the ambient space has upper bound, the estimation of the image radius is obtained, which is the generalization of the corresponding result in Riemannian geometry into Finsler geometry.

关 键 词：FINSLER流形 一致常数 可反常数 T-曲率 法曲率 

分 类 号：O174.56[理学—数学]