局部对称空间中线性Weingarten超曲面

研究了局部对称空间中具有有界平均曲率的线性 Weingarten 超曲面 M^{n}. 通过对 M^{n} 上的对称张量 的模长进行适当限制, 得到了该类超曲面要么是 全脐的, 要么等距于一个具有两个主曲率的超曲面, 且其中一个主曲率的重数为 1.

Linear Weingarten hypersurfaces in locally symmetric manifolds

The complete linear Weingarten hypersurfaces with bounded mean curvature in locally symmetric manifold are studied. By supposing a suitable restriction on the norm of which is symmetric tensor in M^{n}, it is proved that such a hypersurface must be either totally umbilical or isometric to the hypersurface with two distinct principle curvatures, one of which is simple.