局部对称空间中线性Weingarten超曲面
Linear Weingarten hypersurfaces in locally symmetric manifolds
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摘要: 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.Abstract: 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.