【摘要】 本文给出了空间形式F^3+p（c）（P>1）中具有平行平均曲率向量场的三维紧致子流形M³是全脐点的Ricci曲率的Pinching条件。更多还原

【Abstract】 Let F3 +p(c) be a 3+p-dimensional space form with constant sectional curvature C, and let M3 be a 3-dimensional submanifold with parallel mean curvature vector.In this paper, we obtain the following :Theorem 1. Let M3 be a 3-dimensional submanifold in F3+p(c)(c≥0, P>1) with parallel mean curvature vector ξ. If the Ricci curvature of M3is not less than 5/4-(c+ ||ξ||2), then M3 must be totally umbilical. Theorem 2. Let M3 be a 3-dimensional submanifold in F3+p(c)(p>1)with parallel mean curvature vector ξ. If the sectional curvature of M3 is positive and the Ricci curvature of M3 is not less then k(c+||ξ||2) with k =min then M3 is totally umbilical.更多还原