调和映射的刘维尔型定理

A Liouville Type Theorem of Harmonic Maps

摘要:

假设出发流形的径向截曲率Kr满足|Kr(x)|≤k(1-k)r2(x0,x)，这里x0为极点,k为满足一定条件的常数,那么到任意象流形的能量慢发散的调和映射必是常映射.因而它是文献［3 4］中所提到的定理的推广.

Abstract:

Assuming the radial sectional curvature Kr of the target manifold satisfies |Kr(x)|≤k(1-k)r2(x0,x), where x0 is a pole, k is a constant satisfying some conditions, a harmonic map to any image manifold with slowly divergent energy must be constant. Then it improves the theorems of Reference ［3 4］ raised.