Minimal Hypersurfaces in a Riemannian Manifold of Constant Curvature
Minimal Hypersurfaces in a Riemannian Manifold of Constant Curvature
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DOI：
10.2307/2373502
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发表时间：
1970
影响因子：
1.7
通讯作者：
T. Ôtsuki
中科院分区：
文献类型：
--
作者：
T. Ôtsuki
tures和n分别为dim V1 = m> 1和dim V2 =n-m？1.在本陈述的后半部分，第二基本形式A有两个多重性特征值dim VI和dim V2。本文主要研究Sn+1中极小超曲面的匡威问题。本文证明了常曲率黎曼流形中超曲面的主向量空间分布的局部可积性定理（定理2）。利用它，他将研究极小超曲面，使主曲率的重数是常数。他将证明，如果主曲率的数目是2，并且它们的重数至少是2，对于Sn +'中的这种极小超曲面，则它是
tures and n respectively, dim V1 = m> 1 and dim V2 =n-m ?1. Mr n-mn In the latter part of this statement, the second fundamental form A has two eigenvalues of multiplicities dim VI and dim V2. The main purpose of the present paper is to investigate the converse problem for minimal hypersurfaces in Sn+1. The author will prove a local theorem on the integrability of the distributions of the spaces of principal vectors of a hypersurface in a Riemannian manifold of constant curvature (Theorem 2). Making use of it, he will investigate minimal hypersurfaces such that the multiplicities of principal curvatures are constant. He will prove that if the number of principal curvatures is two and the multiplicities of them are at least two for a minimal hypersurface of this kind in Sn+', then it is