Abstract:

With the help of  the Chern connection in Finsler manifolds, we analyzed the convexity of distance function in a Finsler manifold, then discussed harmonic maps between two Finsler manifolds in the point of view of the topology, and obtained a nonexistence theorem about nontrivial harmonic maps from a Finsler manifold with the limited fundamental group to nonfocus Finsler manifold, and  studied some problems on homotopy class of mapping and got a simple existence theorem.

Key words: Finsler manifold, Jacobi field, harmonic maps, focal point