一类具有平行平均曲率和有限全曲率的完备子流形

Some Complete Submanifolds with Parallel Mean Curvature and Finite Total Curvature

本文把Berard P.,do Carmo M.,Santos W.在1998年所得的结果,分别推广到局部对称的Cartan-Hadamard流形中具有常平均曲率和有限全曲率的完备超曲面,以及球面上具有平行平均曲率和有限全曲率的完备子流形.

In this paper, we advanced the result obtained by Berard P., do Carmo M., Santos W. to the complete non-compact orientable hypersurface in a locally symmetric Riemannian manifold with constant mean curvature and finite total curvature, and also to the complete submanifold in a sphere with parallel mean curvature and finite total curvature.