scholarly journals On locally conformally flat gradient steady Ricci solitons

2012 ◽  
Vol 364 (5) ◽  
pp. 2377-2391 ◽  
Author(s):  
Huai-Dong Cao ◽  
Qiang Chen
Keyword(s):  
Ricci Solitons ◽  
Conformally Flat ◽  
Locally Conformally Flat

A note on locally conformally flat gradient Ricci solitons

2013 ◽  
Vol 168 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Manuel Fernández-López ◽  
Eduardo García-Río
Keyword(s):  
Ricci Solitons ◽  
Conformally Flat ◽  
Gradient Ricci Solitons ◽  
Locally Conformally Flat

scholarly journals Conformally Flat Siklos Metrics Are Ricci Solitons

Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 64
Author(s):  
Giovanni Calvaruso
Keyword(s):  
Ricci Soliton ◽  
Ricci Solitons ◽  
Conformally Flat ◽  
Soliton Equation ◽  
Locally Conformally Flat

We study and solve the Ricci soliton equation for an arbitrary locally conformally flat Siklos metric, proving that such spacetimes are always Ricci solitons.

scholarly journals Locally Conformally Flat Lorentzian Gradient Ricci Solitons

2011 ◽  
Vol 23 (3) ◽  
pp. 1196-1212 ◽  
Author(s):  
M. Brozos-Vázquez ◽  
E. García-Río ◽  
S. Gavino-Fernández
Keyword(s):  
Ricci Solitons ◽  
Conformally Flat ◽  
Gradient Ricci Solitons ◽  
Locally Conformally Flat

scholarly journals ON LOCALLY CONFORMALLY FLAT GRADIENT SHRINKING RICCI SOLITONS

2011 ◽  
Vol 13 (02) ◽  
pp. 269-282 ◽  
Author(s):  
XIAODONG CAO ◽  
BIAO WANG ◽  
ZHOU ZHANG
Keyword(s):  
Sectional Curvature ◽  
Ricci Curvature ◽  
Exponential Growth ◽  
Integral Identity ◽  
Ricci Solitons ◽  
Riemannian Curvature ◽  
Conformally Flat ◽  
Gradient Ricci Solitons ◽  
Riemannian Curvature Tensor ◽  
Locally Conformally Flat

In this paper, we first apply an integral identity on Ricci solitons to prove that closed locally conformally flat gradient Ricci solitons are of constant sectional curvature. We then generalize this integral identity to complete noncompact gradient shrinking Ricci solitons, under the conditions that the Ricci curvature is bounded from below and the Riemannian curvature tensor has at most exponential growth. As a consequence, we classify complete locally conformally flat gradient shrinking Ricci solitons with Ricci curvature bounded from below.

scholarly journals $L^{p}$ harmonic 1-forms on conformally flat Riemannian manifolds

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jing Li ◽  
Shuxiang Feng ◽  
Peibiao Zhao
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Finiteness Theorem ◽  
Conformally Flat ◽  
Locally Conformally Flat ◽  
Flat Riemannian Manifold ◽  
Ricci Form

AbstractIn this paper, we establish a finiteness theorem for $L^{p}$ L p harmonic 1-forms on a locally conformally flat Riemannian manifold under the assumptions on the Schrödinger operators involving the squared norm of the traceless Ricci form. This result can be regarded as a generalization of Han’s result on $L^{2}$ L 2 harmonic 1-forms.

A note on 4-dimensional locally conformally flat Walker manifolds

2007 ◽  
Vol 42 (5) ◽  
pp. 270-277 ◽  
Author(s):  
S. Azimpour ◽  
M. Chaichi ◽  
M. Toomanian
Keyword(s):  
Conformally Flat ◽  
Locally Conformally Flat
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