局部对称黎曼流形中具有平行平均曲率向量的子流形

Submanifolds with Parallel Mean Curvature Vector in a Locally Symmetric Riemannian Manifold

设Nn+p 是截面曲率KN 满足12 <δ≤KN ≤ 1的n+p维局部对称完备黎曼流形 ,p≥ 2 .M是Nn+p 的具有平行平均曲率向量的n维紧致子流形 .本文讨论了这类子流形关于第二基本形式模长平方的积分不等式及其Pinching问题 .

Let N n+p  be a (n+p)-dimensional Locally symmetric complete Riemannian manifold with sectional curvature K N such that 12<δ≤K N≤1 Let M be a n-dimensional submanifold with parallel mean curvature vector in N n+p . In this paper we discuss the integral invariant about the square of the norm of the second fundamental form S and its pinching problem.