Rigidity of linear Weingarten hypersurfaces in locally symmetric manifolds

2016 ◽  
Vol 289 (11-12) ◽  
pp. 1309-1324 ◽  
Author(s):  
Luis J. Alías ◽  
Henrique F. de Lima ◽  
Josué Meléndez ◽  
Fábio R. dos Santos
Keyword(s):  
Linear Weingarten Hypersurfaces ◽  
Locally Symmetric Manifolds

scholarly journals LINEAR WEINGARTEN HYPERSURFACES IN A REAL SPACE FORM

2010 ◽  
Vol 52 (3) ◽  
pp. 635-648 ◽  
Author(s):  
SHICHANG SHU
Keyword(s):  
Space Form ◽  
Real Space ◽  
Principal Curvatures ◽  
Riemannian Product ◽  
Rigidity Results ◽  
Linear Weingarten Hypersurfaces

AbstractIn this paper, we investigate linear Weingarten hypersurfaces with two distinct principal curvatures in a real space form Mn+1(c), we obtain two rigidity results and give some characterization of the Riemannian product Sk(a) × Sn−k($\sqrt{1-a^2})\$), 1 ≤ k ≤ n − 1 in Mn+1(c)(c = 1), the Riemannian product Rk × Sn−k(a), 1 ≤ k ≤ n −1 in Mn+1(c)(c = 0) and the Riemannian product Hk(tanh2 ρ−1) × Sn−k(coth2 ρ−1), 1 ≤ k ≤ n −1 in Mn+1(c)(c = −1).

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