中文摘要：

该文讨论了F-稳态映射的Liouville型定理,并证明了当初始流形的截面曲率满足某些非正条件、F满足F-p-条件时,具有有限F能量的F-稳态映射是常值映射.作者也研究了一类特殊的F-稳态映射,即服从积分F-守恒律的映射,并证明了一个类似的Liouville型定理,该定理的曲率假定和F-p-条件和上述定理相同,但F-能量有限性被替换成更弱的F-能量慢发散条件.

英文摘要：

In this paper,the author discusses theorems of Liouville type for F-stationary maps,and proves that F-stationary maps with finite F-energy must be constant,if the sectional curvatures of the initial manifolds satisfy some nonpositive conditions and F obeys the F-p- condition.The author also investigates a class of special F-stationary maps,i.e.,maps obeying the integral F-conservation law,and proves similar theorems of Liouville type,under the same curvature conditions and the F-p-condition,but replacing the finiteness of F-energy by the slowly divergent F-energies.