论文标题
关于Minkowskian Finsler歧管的产品
On Minkowskian Product of Finsler Manifolds
论文作者
论文摘要
令（M_1，F_1）和（M_2，F_2）为一对鳍片歧管。 （M_1，F_1）和（M_2，F_2）相对于产品功能F的Minkowskian产品Finsler歧管（M，F）是产品歧管M = M_1 \ TIMES M_2，赋予了Finsler Metric f^2 = f（k，k，k，k，k，k =（f_1）^2，h =（f_1）^2，h =（f_2，f_2，f_2，f_2）^2。在本文中，（M，F）的cartan连接和Berwald连接是根据（M_1，F_1）和（M_2，F_2）的相应对象得出的。获得了（m，f）的必要条件（M，f）（分别是弱的伯瓦尔德，兰德斯伯格，弱的兰斯伯格）。因此，给出了上面提到的特殊Finsler歧管的有效方法。
Let (M_1,F_1) and (M_2,F_2) be a pair of Finsler manifolds. The Minkowskian product Finsler manifold (M,F) of (M_1,F_1) and (M_2,F_2) with respect to a product function f is the product manifold M=M_1\times M_2 endowed with the Finsler metric F^2=f(K,H), where K=(F_1)^2,H=(F_2)^2. In this paper, the Cartan connection and Berwald connection of (M,F) are derived in terms of the corresponding objects of (M_1,F_1) and (M_2,F_2). Necessary and sufficient conditions for (M,F) to be Berwald (resp. weakly Berwald, Landsberg, weakly Landsberg) manifold are obtained. Thus an effective method for constructing special Finsler manifolds mentioned above is given.
