Some Results On F-harmonic Maps With Potential

In this thesis,by denoting the F-harmonic maps with potential,we mainly study the variation,stability and gap property of F-harmonic maps with potential,then obtain some results.In chapter 1,we denote the F-harmonic maps with potential,and make a general description on the recent reserches from harmonic maps to harmonic maps with potential.In chapter 2,we study the first variation and the second variation of the F-harmonic maps with potential,then obstain some property.In chapter3,we investigate the stable F-harmonic maps with potential from or into general subma-nifolds of the sphere and the Euclidean space.Assuming that all initial manifolds are compact,we prove that this stable F-harmonic maps with potential is contant,if the map satisfies some conditions.In chapter4,we establish a Bochner-typerd formula and use it to study the gap property of F-harmonic maps with potential.