局部对称伪黎曼流形中具有平行平均曲率向量的类空子流形

Space-like submanifolds with parallel mean curvature in locally symmetric pseudo-Riemannian manifold

设N_p^(n+p)为n+p维局部对称完备连通的伪黎曼流形,其截面曲率K_N满足0<δ≤K_N≤1,Mn为N_p^(n+p)中具有平行平均曲率的类空子流形.通过计算第二基本形式的Laplacian,得到这类子流形关于第二基本形式模长平方的积分不等式及极大条件下的Pinching定理.

Np＋p （c） was an （n ＋ p）-dimensional locally symmetric complete pseudo-Riemannian manifold, whose sectional curvature KN satisfied 0〈δ≤KN≤1 was a compact spacelike submanifolds with parallel mean curvature in Npn＋p . By calculating the Laplacian of the second fundamental form of Mn, an integral inequality and a pinching theorem about the square of the norm of the second fundamental form of Mn were obtained in this paper.