Characterizations of Spacelike Submanifolds with Constant Scalar Curvature in the de Sitter Space

2017 ◽  
Vol 15 (1) ◽  
Author(s):  
Luis J. Alías ◽  
Henrique F. de Lima ◽  
Fábio R. dos Santos
Keyword(s):  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
De Sitter Space ◽  
De Sitter ◽  
Spacelike Submanifolds

Complete spacelike hypersurfaces in a de Sitter space

2006 ◽  
Vol 73 (1) ◽  
pp. 9-16 ◽  
Author(s):  
Shu Shichang
Keyword(s):  
Scalar Curvature ◽  
Mean Curvature ◽  
Constant Scalar Curvature ◽  
De Sitter Space ◽  
De Sitter ◽  
Principal Curvatures ◽  
Complete Spacelike Hypersurfaces ◽  
Spacelike Hypersurfaces ◽  
The Mean

In this paper, we characterise the n-dimensional (n ≥ 3) complete spacelike hypersurfaces Mn in a de Sitter space with constant scalar curvature and with two distinct principal curvatures. We show that if the multiplicities of such principal curvatures are greater than 1, then Mn is isometric to Hk (sinh r) × Sn−k (cosh r), 1 < k < n − 1. In particular, when Mn is the complete spacelike hypersurfaces in with the scalar curvature and the mean curvature being linearly related, we also obtain a characteristic Theorem of such hypersurfaces.

A gap theorem for complete constant scalar curvature hypersurfaces in the de Sitter space

2001 ◽  
Vol 37 (3) ◽  
pp. 237-250 ◽  
Author(s):  
Aldir Brasil ◽  
A. Gervasio Colares ◽  
Oscar Palmas
Keyword(s):  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
De Sitter Space ◽  
De Sitter ◽  
Gap Theorem

scholarly journals Complete maximal spacelike surfaces in an anti-de Sitter space {\bf H}^{4}_{2}(c)

2000 ◽  
Vol 42 (1) ◽  
pp. 139-156
Author(s):  
Qing-Ming Cheng
Keyword(s):  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
De Sitter Space ◽  
Second Fundamental Form ◽  
Spacelike Surface ◽  
De Sitter ◽  
Totally Geodesic ◽  
The Second Fundamental Form ◽  
Spacelike Surfaces ◽  
Hyperbolic Cylinder

In this paper, we prove that if M^2 is a complete maximal spacelike surface of an anti-de Sitter space {\bf H}^{4}_{2}(c) with constant scalar curvature, then S=0, S={-10c\over 11}, S={-4c\over 3} or S=-2c, where S is the squared norm of the second fundamental form of M^{2}. Also(1) S=0 if and only if M^2 is the totally geodesic surface {\bf H}^2(c);(2) S={-4c\over 3} if and only if M^2 is the hyperbolic Veronese surface;(3) S=-2c if and only if M^2 is the hyperbolic cylinder of the totally geodesicsurface {\bf H}^{3}_{1}(c) of {\bf H}^{4}_{2}(c).1991 Mathematics Subject Classifaction 53C40, 53C42.

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