以数量曲率为正的闭黎曼流形为出发流形的F-调和映射

F-harmonic Maps from Closed Riemannian Manifold with Positive Scalar Curvature

众所周知从一个Ricci曲率为正的闭黎曼流形到一个截面曲率非正的完备黎曼流形之间是不存在非常值调和映射的.进一步Yang Qi-lin给出了从一个数量曲率为正的闭黎曼流形到一个截面曲率非正的完备黎曼流形之间存在非常值调和映射的结果.该文则研究了以这一类流形为出发流形的F-调和映射,得到从一个数量曲率为正的闭黎曼流形到一个截面曲率非正的完备黎曼流形之间存在非常值F-调和映射的结果,从而推广了调和映射的一些结果.

It is well known that there is no non-constant harmonic maps from a closed Riemannian manifold of positive Ricci curvature to a complete Riemannian manifold with non-positive sectional curvature. Qilin Yang has given out the result if maps from a closed Riemannian manifold of positive scalar curvature to a complete Riemannian manifold with non-positive sectional curvature is a non-constant harmonic maps. This paper gives out the result if F-harmonic maps from these manifold are non-constant harmonic maps, which generalizes other author＇s results.