scholarly journals A new characterization of complete linear Weingarten hypersurfaces in real space forms

2013 ◽  
Vol 261 (1) ◽  
pp. 33-43 ◽  
Author(s):  
Cícero Aquino ◽  
Henrique de Lima ◽  
Marco Velásquez
Keyword(s):  
Real Space ◽  
Space Forms ◽  
Linear Weingarten Hypersurfaces ◽  
Real Space Forms

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).

scholarly journals A Class of Special Hypersurfaces in Real Space Forms

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Yan Zhao ◽  
Ximin Liu
Keyword(s):  
Real Space ◽  
Principal Curvatures ◽  
Space Forms ◽  
Isoparametric Hypersurfaces ◽  
Real Space Forms ◽  
Constant Principal Curvatures

We define the generalized golden- and product-shaped hypersurfaces in real space forms. A hypersurfaceMin real space formsRn+1,Sn+1, andHn+1is isoparametric if it has constant principal curvatures. Based on the classification of isoparametric hypersurfaces, we obtain the whole families of the generalized golden- and product-shaped hypersurfaces in real space forms.

scholarly journals A fundamental theorem for submanifolds of multiproducts of real space forms

2017 ◽  
Vol 17 (3) ◽  
Author(s):  
Marie-Amélie Lawn ◽  
Julien Roth
Keyword(s):  
Minimal Surfaces ◽  
Fundamental Theorem ◽  
Arbitrary Number ◽  
Real Space ◽  
Isometric Immersions ◽  
Space Forms ◽  
Real Space Forms ◽  
Simply Connected ◽  
Bonnet Theorem

AbstractWe prove a Bonnet theorem for isometric immersions of submanifolds into the products of an arbitrary number of simply connected real space forms. Then we prove the existence of associate families of minimal surfaces in such products. Finally, in the case of 𝕊

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