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.

Solutions of the Ricci soliton equation for a large class of Siklos spacetimes

2021 ◽  
pp. 2150052
Author(s):  
Giovanni Calvaruso
Keyword(s):  
Large Class ◽  
Vector Fields ◽  
Killing Vector ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Killing Vector Fields ◽  
Soliton Equation

We determine and describe all the Ricci solitons within a very large class of Siklos metrics. As an application, the Ricci soliton equation is completely solved for several classes of Siklos metrics admitting additional Killing vector fields (in particular, for several homogeneous ones).

scholarly journals η-Ricci Solitons on Sasakian 3-Manifolds

2017 ◽  
Vol 55 (2) ◽  
pp. 143-156
Author(s):  
Pradip Majhi ◽  
Uday Chand De ◽  
Debabrata Kar
Keyword(s):  
Ricci Tensor ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Conformally Flat ◽  
Curvature Condition ◽  
Cyclic Parallel Ricci Tensor ◽  
Codazzi Type ◽  
Parallel Ricci Tensor

AbstractIn this paper we studyη-Ricci solitons on Sasakian 3-manifolds. Among others we prove that anη-Ricci soliton on a Sasakian 3-manifold is anη-Einstien manifold. Moreover we considerη-Ricci solitons on Sasakian 3-manifolds with Ricci tensor of Codazzi type and cyclic parallel Ricci tensor. Beside these we study conformally flat andφ-Ricci symmetricη-Ricci soliton on Sasakian 3-manifolds. Alsoη-Ricci soliton on Sasakian 3-manifolds with the curvature conditionQ.R= 0 have been considered. Finally, we construct an example to prove the non-existence of properη-Ricci solitons on Sasakian 3-manifolds and verify some results.

scholarly journals RICCI SOLITONS AND CONTACT METRIC MANIFOLDS

2012 ◽  
Vol 55 (1) ◽  
pp. 123-130 ◽  
Author(s):  
AMALENDU GHOSH
Keyword(s):  
Vector Field ◽  
Sectional Curvature ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Conformally Flat ◽  
Contact Metric Manifold ◽  
Potential Vector ◽  
Contact Metric Manifolds ◽  
Potential Vector Field

AbstractWe study on a contact metric manifold M2n+1(ϕ, ξ, η, g) such that g is a Ricci soliton with potential vector field V collinear with ξ at each point under different curvature conditions: (i) M is of pointwise constant ξ-sectional curvature, (ii) M is 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 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 SOME TYPES OF η-RICCI SOLITONS ON LORENTZIAN PARA-SASAKIAN MANIFOLDS

2018 ◽  
Vol 33 (2) ◽  
pp. 217
Author(s):  
Abhishek Singh ◽  
Shyam Kishor
Keyword(s):  
Vector Field ◽  
Einstein Manifold ◽  
Sasakian Manifold ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Conformally Flat ◽  
Sasakian Manifolds ◽  
Potential Vector ◽  
3 Dimensional ◽  
Potential Vector Field

In this paper we study some types of  η-Ricci solitons on Lorentzianpara-Sasakian manifolds and we give an example of  η-Ricci solitons on 3-dimensional Lorentzian para-Sasakian manifold. We obtain the conditions of  η-Ricci soliton on ϕ-conformally flat, ϕ-conharmonically flat and ϕ-projectivelyflat Lorentzian para-Sasakian manifolds, the existence of η-Ricci solitons implies that (M,g) is  η-Einstein manifold. In these cases there is no Ricci solitonon M with the potential vector field

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.

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