局部对称黎曼流形中具有平行中曲率向量的子流形

The 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≥ 1.M是Nn + p的具有平行中曲率向量的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 an n+p-dimensional locally symmetric complete Riemannian marifold that its sectional curvature K N Satisfies 12<δ≤K N≤1 and M be an n-dimensinal submanifold with parallel mean curvature vector in N n+p .In the paper,we discuss the integral invariant about the square of the norm of the second fundamental form S and the pinching problem of the submanifolds with parallel mean curvature vector in N n+p .