Hypersurfaces with constant scalar curvature in space forms
Hypersurfaces with constant scalar curvature in space forms
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DOI：
10.1007/bf01444243
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发表时间：
1996-05
影响因子：
1.4
通讯作者：
L. Haizhong
中科院分区：
文献类型：
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作者：
L. Haizhong
设Rn+ l (c)是一个（n+ 1）维的黎曼流形具有恒定的截面曲率c，我们也称它为空间形式。当c—1时，R′′+ l (c)= S′′+ l（即（n+ 1）维单位球空间）；当c= 0时，Rn+ t (c)= E n+ l（即（n+ 1）维欧几里德空间）。设M是Rn+ l (c)中的一个n维紧致超曲面，el.....e， M上的局部正交坐标系域，col.....控制它的对偶共框域。那么M的第二种基本形式是
Let Rn+ l (c) be an (n+ 1)-dimensional Riemannian manifold with constant sectional curvature c, we also call it space form. When c--1, R"+ l (c)= S"+ l (ie (n+ 1)-dimensional unit sphere space); when c= O, Rn+ t (c)= E n+ l (ie (n+ 1)-dimensional Euclidean space). Let M be an n-dimensional compact hypersurface in Rn+ l (c), and el..... e,, a local orthonormal frame field on M, col..... con its dual coframe field. Then the second fundamental form of M is