The scalar curvature of minimal hypersurfaces in spheres

1983 ◽  
Vol 266 (1) ◽  
pp. 105-113 ◽  
Author(s):  
Chia-Kuei Peng ◽  
Chuu-Lian Terng
Keyword(s):  
Scalar Curvature ◽  
Minimal Hypersurfaces ◽  
Hypersurfaces In Spheres

THE SCALAR CURVATURE OF MINIMAL HYPERSURFACES IN A UNIT SPHERE

2007 ◽  
Vol 09 (02) ◽  
pp. 183-200 ◽  
Author(s):  
YOUNG JIN SUH ◽  
HAE YOUNG YANG
Keyword(s):  
Scalar Curvature ◽  
Unit Sphere ◽  
Constant Scalar Curvature ◽  
Minimal Hypersurface ◽  
Second Fundamental Form ◽  
Geodesic Sphere ◽  
Clifford Torus ◽  
Totally Geodesic ◽  
Minimal Hypersurfaces ◽  
The Second Fundamental Form

In this paper, we study n-dimensional compact minimal hypersurfaces in a unit sphere Sn+1(1) and give an answer for S. S. Chern's conjecture. We have shown that [Formula: see text] if S > n, and prove that an n-dimensional compact minimal hypersurface with constant scalar curvature in Sn+1(1) is a totally geodesic sphere or a Clifford torus if [Formula: see text], where S denotes the squared norm of the second fundamental form of this hypersurface.

scholarly journals scalar curvature of minimal hypersurfaces in a sphere

2007 ◽  
Vol 14 (3) ◽  
pp. 423-432 ◽  
Author(s):  
Si-Ming Wei ◽  
Hong-Wei Xu
Keyword(s):  
Scalar Curvature ◽  
Minimal Hypersurfaces
Sign in / Sign up

Export Citation Format

Share Document