Equivariant Minimal S～3 With Constant Curvature In CP～3

In the present paper the equivariant minimal immersion from the Euclideansphere S~3=SU(2) with constant curvature c into the complex projective spaceCP~3 is studied. It is proved that the immersion has to be Lagrangian and hence istotally geodesic.The thesis is divided into two sections. In section 1, as an introduction, thehistorical background of the problem and the principal method used in this thesis arestated, and the main result as well. Firstly, in section 2 the conception of equivariantimmersion from the Euclidean sphere S~3 as Lie group SU(2) into CP~3 isintroduced. Secondly, as the preliminaries for further study, the structure equationsand some basic formulas of the equivariant minimal submanifold S~3 with constantcurvature c in CP~3 are presented. Lastly, the proof of the main theorem is given.