L-可约的Finsler空间向与C可约的Finsler空间的转化-重庆师范大学学报（自然科学版）

文章信息/Info

Author(s):: TONG Yin; College of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, China

摘要:: 可约的Finsler空间一定是可约的Finsler空间，反之则不然。本文研究反面情形的成立条件，实现了可约的Finsler空间向可约的Finsler空间的三种转化。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：可约的Finsler空间，若满足 ,其中，则它是可约的.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可约Finsler空间一定是可约的，并得到平均Cartan挠率的表达式

Abstract:: It is well kowned that C-reducible Finsler space must to 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. First, 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 comparing the relation between the Landsberg curvature and the Cartan torsion, this paper gets a sepecial corollary: If the L-reducible Finsler space satisefies , where , 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 Cartan torsion