A Möbius scalar curvature rigidity on compact conformally flat hypersurfaces in Sn+1

2018 ◽  
Vol 466 (1) ◽  
pp. 762-775
Author(s):  
Limiao Lin ◽  
Tongzhu Li ◽  
Changping Wang
Keyword(s):  
Scalar Curvature ◽  
Conformally Flat ◽  
Scalar Curvature Rigidity

scholarly journals On scalar curvature rigidity of vacuum static spaces

2015 ◽  
Vol 365 (3-4) ◽  
pp. 1257-1277 ◽  
Author(s):  
Jie Qing ◽  
Wei Yuan
Keyword(s):  
Scalar Curvature ◽  
Scalar Curvature Rigidity

scholarly journals Remarks on a scalar curvature rigidity theorem of Brendle and Marques

2013 ◽  
Vol 17 (3) ◽  
pp. 457-470 ◽  
Author(s):  
Graham Cox ◽  
Pengzi Miao ◽  
Luen-Fai Tam
Keyword(s):  
Scalar Curvature ◽  
Rigidity Theorem ◽  
Scalar Curvature Rigidity

COMPACT LOCALLY CONFORMALLY FLAT RIEMANNIAN MANIFOLDS

2001 ◽  
Vol 33 (4) ◽  
pp. 459-465 ◽  
Author(s):  
QING-MING CHENG
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Riemannian Manifolds ◽  
Space Form ◽  
Constant Scalar Curvature ◽  
Topological Classification ◽  
Conformally Flat ◽  
Riemannian Product ◽  
Locally Conformally Flat

First, we shall prove that a compact connected oriented locally conformally flat n-dimensional Riemannian manifold with constant scalar curvature is isometric to a space form or a Riemannian product Sn−1(c) × S1 if its Ricci curvature is nonnegative. Second, we shall give a topological classification of compact connected oriented locally conformally flat n-dimensional Riemannian manifolds with nonnegative scalar curvature r if the following inequality is satisfied: [sum ]i,jR2ij [les ] r2/(n−1), where [sum ]i,jR2ij is the squared norm of the Ricci curvature tensor.

scholarly journals Conformally flat 3-manifolds with constant scalar curvature II

2001 ◽  
Vol 27 (2) ◽  
pp. 387-404
Author(s):  
Qing-Ming CHENG ◽  
Susumu ISHIKAWA ◽  
Katsuhiro SHIOHAMA
Keyword(s):  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
Conformally Flat

HYPERSURFACES IN A UNIT SPHERE Sn+1(1) WITH CONSTANT SCALAR CURVATURE

2001 ◽  
Vol 64 (3) ◽  
pp. 755-768 ◽  
Author(s):  
QING-MING CHENG
Keyword(s):  
Scalar Curvature ◽  
Unit Sphere ◽  
Constant Scalar Curvature ◽  
Second Fundamental Form ◽  
Conformally Flat ◽  
Principal Curvatures ◽  
The Second Fundamental Form ◽  
Locally Conformally Flat ◽  
Complete Hypersurfaces ◽  
Conformally Flat Hypersurface

The paper considers n-dimensional hypersurfaces with constant scalar curvature of a unit sphere Sn−1(1). The hypersurface Sk(c1)×Sn−k(c2) in a unit sphere Sn+1(1) is characterized, and it is shown that there exist many compact hypersurfaces with constant scalar curvature in a unit sphere Sn+1(1) which are not congruent to each other in it. In particular, it is proved that if M is an n-dimensional (n > 3) complete locally conformally flat hypersurface with constant scalar curvature n(n−1)r in a unit sphere Sn+1(1), then r > 1−2/n, and(1) when r ≠ (n−2)/(n−1), ifthen M is isometric to S1(√1−c2)×Sn−1(c), where S is the squared norm of the second fundamental form of M;(2) there are no complete hypersurfaces in Sn+1(1) with constant scalar curvature n(n−1)r and with two distinct principal curvatures, one of which is simple, such that r = (n−2)/(n−1) and

Sign in / Sign up

Export Citation Format

Share Document