本文研究了伪黎曼空间型中具有常平均曲率的类空子流形，得到了这类空子流形的一个积分不等式及刚性定理。

This paper discusses the space-like submanifolds with constant mean curvature in a pseudo-Riemannian space form, and obtain an integrate inequality and a rigidity theorem.

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在黎曼流形上分别给出了伪不变凸函数和弱向量似变分不等式的概念。

The definitions of pseudo-invex function and weak vector variation-like inequality on Riemannian manifolds are presented.

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使得对拟常曲率黎曼流形中紧致子流形的研究由极小子流形和伪脐子流形情形扩展到具有平行平均曲率向量的情形。

The work makes the study of compact submanifolds in quasi constant curvature Riemannian manifolds extend from the especial case to general case.

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