【摘要】 研究拟常曲率黎曼流形中具有平行平均曲率向量的紧致子流形.通过计算子流形第二基本形式模长平方的拉普拉斯,利用Stokes定理,得到这类子流形的一个积分不等式.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.更多还原

【Abstract】 The compact submanifolds in quasi constant curvature Riemannian manifolds with Parallel Mean Curature Vector were studied. By using Stokes theorem, and some last results of algebra inequation, an integral inequality was obtained. The work makes the study of compact submanifolds in quasi constant curvature Riemannian manifolds extend from the especial case to general case.更多还原