scholarly journals ON RIEMANNIAN MANIFOLDS WITH CONSTANT SCALAR CURVATURE ADMITTING A CONFORMAL TRANSFORMATION GROUP

1966 ◽  
Vol 55 (3) ◽  
pp. 472-476 ◽  
Author(s):  
K. Yano
Keyword(s):  
Scalar Curvature ◽  
Riemannian Manifolds ◽  
Conformal Transformation ◽  
Transformation Group ◽  
Constant Scalar Curvature

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 ON RICCI-BOURGUIGNON h-ALMOST SOLITONS IN RIEMANNIAN MANIFOLDS

2020 ◽  
Vol 20 (3) ◽  
pp. 673-680
Author(s):  
YASEMIN SOYLU
Keyword(s):  
Vector Field ◽  
Scalar Curvature ◽  
Riemannian Manifolds ◽  
Integral Formula ◽  
Constant Scalar Curvature ◽  
Ricci Soliton ◽  
Almost Ricci Soliton ◽  
Structure Equations ◽  
Isometric To A Sphere

In this paper, we shall give some structure equations for RB h-almost solitons which generalize previous results for Ricci almost solitons. As a consequence of these equations we also derive an integral formula for the compact gradient RB h-almost solitons which enables us to show that a compact nontrivial almost Ricci soliton is isometric to a sphere provided either it has constant scalar curvature or its associated vector field is conformal.

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