L-可约的Finsler空间向C-可约的Finsler空间的转化  

Turn L-reducible Finsler Space to Be C-reducible Finsler Space

作　　者：童殷[1] 

机构地区：[1]重庆师范大学数学与计算机科学学院,重庆400047

出　　处：《重庆师范大学学报（自然科学版）》2009年第2期58-60,共3页Journal of Chongqing Normal University:Natural Science

基　　金：重庆师范大学青年教师基金(No.07XLQ05)

摘　　要：C-可约的Finsler空间一定是L-可约的Finsler空间,反之则不然。本文研究反面情形的成立条件,实现了L-可约的Finsler空间向C-可约的Finsler空间的3种转化。L-可约的Finsler空间,若分别具有迷向Landsberg曲率、常曲率,则它能转化为C-可约的Finsler空间;在上述两种情形下,通过对比Landsberg曲率和Cartan挠率的关系,得到推论:L-可约的Finsler空间,若满足L∶0∶0+k(x,y)C=0,其中k(x,λy)=λ3k(x,y),则它是C-可约的。在第二种情形的启发下,考虑到常曲率和标量曲率的关系,最后得到具有标量曲率的L-可约Finsler空间一定是C-可约的,并得到平均Cartan挠率的表达式Ik=-1/(Kf2)(Jk∶0+f2/3(n+1)K.k)。It is well kown that C-reducible Finsler space must be L-reducible Finsler space, but the opposite is not true. This paper studies the conditions for the opposite turning to be true. It contains that under three different conditions the L-reducible Finsler space can turn to be C-reducible Finsler space. Firstly, considering that Finsler space with isotropic Landsberg curvature is related with Cartan torsion and Landsberg curvature,so it may turn to be related with mean Cartan torsion and mean Landsberg curvature, it gets Theorem 1. If the L-reducible Finsler space is with isotropic Landsberg curvature, it must turn to be C-reducible Finsler space. Then, the author studies L-reducible Finsler space with constant curvature, and proves that it can turn to be C-reducible Finsler space too. Under such two cases, through comparson of the relation between the Landsberg curvature and the Cartan torsion, this paper gets a sepecial corollary. If the L-reducible Finsler space satisefies L：0：0 ＋ k（x,y）C = 0, where k（x,λy） = λ^3 k（x,y）, it must be C- reducible Finsler space. At last, being inspired by Theorem 2, the author considers the relation between constant cuvature and scalar cuvature, and finds that L-reducible Finsler space with scalar cuvature is also C-reducible Finsler space, and gets the form of the mean Caftan torsion Ik=1/Kf^2（Jk：0＋f^2/3（n＋1）K.k）

关 键 词：C-可约 L-可约 迷向Landsberg曲率 标量曲率 

分 类 号：O186.14[理学—数学]