局部对称空间中的紧致子流形

THE COMPACT SUBMANIFOLD IN A LOCALLY-SYMMETRIC SPACE

本文研究了局部对称空间中的紧致子流形.通过计算子流形的第二基本形式长度的平方的Laplacian,削减了全测地子流形的充分条件"具有平行平均曲率向量"和"极小",获得了这种紧致子流形是局部对称空间全测地子流形的一个充分条件,推广和改进了局部对称空间中全测地子流形的外围空间.

In this paper, the compact submanifold in a locally-symmetric space is researched. By calculating the Laplacian about the square of the norm of the second fundamental form of submanifolds, a necessary condition on the compact submanifold in a locally-symmetric space is given without the condition ＂with parallel mean curvature vector＂ and ＂minimal＂ , which can generalize and improve the outer space of totally geodesic in a locally-symmetric space.