局部对称空间中线性Weingarten超曲面

Linear Weingarten Hypersurfaces in Locally Symmetric Manifolds

研究了局部对称空间中具有有界平均曲率的可定向完备线性Weingarten超曲面的刚性分类.在对超曲面的全脐张量Φ的模长进行适当限制下,应用广义极大值原理,得到了该类超曲面是全脐的或等距于一个具有2个不同主曲率的超曲面,且其中一个主曲率的重数为1.

The rigidity classifications for complete orientable linear Weingarten hypersurfaces with bounded mean curvature in locally symmetric manifold are studied. By supposing a suitable restriction on the norm of the totally umbilical tensor Φ and using the generalized maximum principle,it is proved that such a hypersurface must be either totally umbilical or isometric to the hypersurface with two distinct principal curvatures,one of which is simple.