CONGRUENCE THEOREMS FOR PROPER SEMI- RIEMANNIAN HYPERSURFACES IN A REAL SPACE FORM
CONGRUENCE THEOREMS FOR PROPER SEMI- RIEMANNIAN HYPERSURFACES IN A REAL SPACE FORM
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发表时间：
1987
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通讯作者：
N. Abe;N. Koike;S. Yamaguchi
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作者：
N. Abe;N. Koike;S. Yamaguchi
对于实空间形式中的黎曼超曲面，一些作者在某些假设下研究了与全等相关的问题。P. J. 瑞安（[2]，[3]）在实空间形式中为形状算子至多有两个互不相同的常特征值的黎曼超曲面建立了一个局部全等定理。对于半黎曼实空间形式中的半黎曼超曲面考虑这个问题是一个自然的问题。本文的主要目的是得到一个与瑞安的定理类似的适定半黎曼超曲面的全等定理。在本文中，所有流形都是光滑且连通的，并且除非另有说明，几何对象都假定是光滑的。
For Riemannian hypersurfaces in a real space form, several authors investigated problems related to congruity under some assumptions. P. J. Ryan ([2], [3]) established a local congruence theorem in a real space form for Riemannian hypersurfaces whose shape operators have at most two mutually distinct constant eigenvalues. It is a natural question to consider this problem for semiRiemannian hypersurfaces in a semi-Riemannian real space form. The main purpose of this paper is obtain a congruence theorem for proper semi-Riemannian hypersurfaces analogous to that of Ryan. Throughout this paper, all manifolds are smooth and connected and geometrical objects are assumed to be smooth unless mentioned otherwise.