On 3-Dimensional Totally Real Minimal Submanifolds in a Complex Projective Space

Let CP^3+p be a complex (3+p)-dimensional complex projective space with the Fubini-Study metric of constant homomorphic sectional curvature 1, and M³ be a real 3-dimensional totally compact and real minimal submanifold in CP^3+p. In this paper, some pinching theorems for the Ricci curvature and the scalar curvature of M³ in CP^3+p are given. It is shown that if the Ricci curvature of M³ in CP³ is larger than 1/6, then M³ is totally geodesic in CP³.