闵可夫斯基积芬斯勒流形的嘉当挠率

Cartan Torsion of Minkowskian Product Finsler Manifold

设(M1, F1)和(M2, F2)是两个芬斯勒流形, 闵可夫斯基积芬斯勒度量是在乘积流形 M=M1×M2上赋予的芬斯勒度量 F=√f(K,H), 其中K=F12, H=F22, 且f是积函数. 本文主要研究闵可夫斯基积芬斯勒流形(M,F)的嘉当挠率和平均嘉当挠率, 利用张量分析法, 得到了闵可夫斯基积芬斯勒流形 (M,F)的嘉当挠率消失的必要条件;在 (M1, F1)和(M2, F2)的平均嘉当挠率消失的条件下, 给出了闵可夫斯基积芬斯勒流形 (M,F)的平均嘉当挠率消失的充分条件, 从而给出了一种刻画具有特殊性质的芬斯勒流形的有效方法.

Let (M1, F1) and (M2, F2) be two Finsler manifolds, Minkowskian product Finsler metric is the Finsler metric F=√f(K,H) endowed on the product manifold M = M1 ×M2, where K=F12, H=F22, and f is product function. In this paper, we study Cartan torsion and mean Cartan torsion of Minkowskian product Finsler manifold (M,F). By using tensor analysis, we obtain the necessary condition that Minkowskian product Finsler manifold (M,F) has vanishing Cartan torsion. Also, we give the sufficient con- dition that Minkowskian product Finsler manifold (M,F) has vanishing mean Cartan torsion under the conditions of Finsler manifolds (M1, F1) and (M2, F2) have vanishing mean Cartan torsion. Then an effective method for characterise Finsler manifolds with special property is given.