Equivariant Weakly Lagrangian Minimal S～3 In CP～4

In this paper, the equivariant weakly Lagrangian minimal S~3 in CP~4 are completely classified and the analytic expressions of the corresponding immersion φ : S~3→ CP~4 are given.The thesis is divided into six sections. The introduction presents the historical background of the problem, the principal research method and the main research result as well. The first section introduces the equivariant submanifold S~3 and does a research into the structure equations of the equivariant weakly Lagrangian submanifold S~3 as the preliminaries for further study. The second section presents basic formulas that gives the relationship between the second fundamental form and curvature .The third and forth sections finish the proof of theory A, and give the classifications and analytic expressions as the curvature is non-constant .The fifth section proves the theory B,and presents the analytic expressions when the curvature is constant.