New characterizations for hyperbolic cylinders in anti-de Sitter spaces

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• 作者：R.M.B. Chaves^a ; ^{rosab@ime.usp.br} ; ; L.A.M. Sousa Jr.^b ; ^{amancio@impa.br} ; ; B.C. Valé ; rio^a ; ^{barbarav@ime.usp.br} ;
• 关键词：Anti-de Sitter space ; Complete spacelike hypersurfaces ; Gauss&ndash ; Kronecker curvature ; Scalar curvature
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2012
• 期刊代码：76_0022247x
• 类别：mt
• 出版时间：1 September, 2012
• 卷：393
• 期：1
• 页码：166-176
• 文件大小：257 K

摘要

In this paper we study complete maximal spacelike hypersurfaces in anti-de Sitter space with either constant scalar curvature or constant non-zero Gauss-Kronecker curvature. We characterize the hyperbolic cylinders , as the only such hypersurfaces with () principal curvatures with the same sign everywhere. In particular we prove that a complete maximal spacelike hypersurface in with negative constant Gauss-Kronecker curvature is isometric to .