Minkowski空间的等价性定理及在Finsler几何的应用  

On Equivalence Theorems of Minkowski Spaces and Applications in Finsler Geometry

作　　者：李明 Ming LI(School of Science,Chongqing University of Technology, Chongqing 400054,P.R.China)

机构地区：[1]重庆理工大学理学院,重庆400054

出　　处：《数学学报（中文版）》2019年第2期177-190,共14页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11501067;11571184);the Marie Cuire IRSES project(PIRSES-GA-2012-317721-LIE-DIFF-GEOM)

摘　　要：首先利用中心仿射几何中的结果建立了Minkowski空间的等价性定理.作为在Finsler几何中的应用,我们证明满足一定条件的Landsberg空间为Berwald空间,这些条件可以是具有闭的Cartan型形式,S曲率为零或平均Berwald曲率为零.We first establish an equivalence theorem of Minkowski spaces by using results in centro-affine differential geometry. As applications in Finsler geometry, we prove that a Finsler manifold is a Berwald space if it is a Landsberg space and satisfies one of the following conditions: closed Cartan-type form, vanishing S curvature or vanishing mean Berwald curvature.

关 键 词：MINKOWSKI空间 卵形超曲面 Cartan型形式 平行移动 Berwald空间 

分 类 号：O186.14[理学—数学]