Spacelike hypersurfaces with constant scalar curvature

1998 ◽  
Vol 95 (4) ◽  
pp. 499-505 ◽  
Author(s):  
Qing-Ming Cheng ◽  
Susumu Ishikawa
Keyword(s):  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
Spacelike Hypersurfaces

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.

Spacelike hypersurfaces with constant scalar curvature

1998 ◽  
Vol 95 (1) ◽  
pp. 499-505 ◽  
Author(s):  
Qing-Ming Cheng ◽  
Susumu Ishikawa
Keyword(s):  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
Spacelike Hypersurfaces
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