局部对称空间中的紧致极小子流形

Compact minimal submanifolds in locally symmetric spaces

设Nn+p(c)为n+p维的常曲率空间,Mn为Nn+p(c)中的n维紧致极小子流形,Yau得到了一个Simons不等式相对应的结论,本文将常曲率空间的类似问题推广到局部对称空间中,得到了两个主要定理.

Let M^n be an n- dimensional compact minimal submanifold immersed in a manifold N^n-p with constant curvature c. Yau obtains an inequality opposite to that of Simons. In this paper ,the similar problems in space of constant curvature are popularized in the space of locally symmetry.