Abstract:

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.

Key words: F-stationary map, Theorem of Liouville type, F-harmonic map