Finsler流形间调和映射的拓扑性质

Some Topology Properties of Harmonic Map in Finsler Manifolds

利用Finsler流形上的Chern联络,通过分析流形上距离函数的凸性,研究Finsler流形间的调和映射,得到一个从具有有限基本群Finsler流形到无焦点Finsler流形的非平凡调和映射的不存在性定理,进而讨论了一个同伦类中调和映射的存在性问题.

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.