scholarly journals A deformation of tori with constant mean curvature in ${\bf R}\sp 3$ to those in other space forms

1992 ◽  
Vol 330 (2) ◽  
pp. 845-857
Author(s):  
Masaaki Umehara ◽  
Kotaro Yamada
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Space Forms

scholarly journals Biharmonic Hypersurfaces in Pseudo-Riemannian Space Forms with at Most Two Distinct Principal Curvatures

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Chao Yang ◽  
Jiancheng Liu
Keyword(s):  
Euclidean Space ◽  
Mean Curvature ◽  
Riemannian Space ◽  
Constant Mean Curvature ◽  
Space Form ◽  
De Sitter Space ◽  
De Sitter ◽  
Principal Curvatures ◽  
Space Forms ◽  
Riemannian Space Forms

In this paper, we show that biharmonic hypersurfaces with at most two distinct principal curvatures in pseudo-Riemannian space form Nsn+1c with constant sectional curvature c and index s have constant mean curvature. Furthermore, we find that such biharmonic hypersurfaces Mr2k−1 in even-dimensional pseudo-Euclidean space Es2k, Ms−12k−1 in even-dimensional de Sitter space Ss2kcc>0, and Ms2k−1 in even-dimensional anti-de Sitter space ℍs2kcc<0 are minimal.

Biharmonic hypersurfaces in pseudo-Riemannian space forms

2016 ◽  
Vol 13 (07) ◽  
pp. 1650094 ◽  
Author(s):  
Dan Yang ◽  
Yu Fu
Keyword(s):  
Sectional Curvature ◽  
Mean Curvature ◽  
Riemannian Space ◽  
Constant Mean Curvature ◽  
Space Form ◽  
Constant Sectional Curvature ◽  
Principal Curvatures ◽  
Space Forms ◽  
Riemannian Space Forms

Let [Formula: see text] be a nondegenerate biharmonic pseudo-Riemannian hypersurface in a pseudo-Riemannian space form [Formula: see text] with constant sectional curvature [Formula: see text]. We show that [Formula: see text] has constant mean curvature provided that it has three distinct principal curvatures and the Weingarten operator can be diagonalizable.

scholarly journals Discrete constant mean curvature nets in space forms: Steiner’s formula and Christoffel duality

2014 ◽  
Vol 52 (4) ◽  
pp. 612-629 ◽  
Author(s):  
Alexander I. Bobenko ◽  
Udo Hertrich-Jeromin ◽  
Inna Lukyanenko
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Space Forms
Sign in / Sign up

Export Citation Format

Share Document