Equivariant Harmonic Maps

In this paper,we mainly study equivariant harmonic maps,the theorem of reduction, the equivariant variational formula,and the harmonic equation.Then we investigate the theorem of reduction and the equivariant variational formula of Fharmonic maps.This paper is divided into six parts:In chapter 1,we will make a general description of the recent researches in our field.In chapter 2,we introduce the Riemann immersion and equivariant harmonic maps.In chapter 3,we prove the theorem of reduction of equivariant harmonic maps.In chapter 4,we calculate the equivariant variational formula of harmonic maps.In chapter 5,we introduce the ordinary differential equation which is constructed by Smith.In chapter 6,we prove the theorem of reduction and the variational formula of equivariant harmonic maps.