Conformally Flat Ricci Solitons on Lie Groups with Left-invariant (pseudo)Riemannian Metrics

2016 ◽  
Author(s):  
Pavel Klepikov ◽  
◽  
Dmitry Oskorbin ◽  
Keyword(s):  
Lie Groups ◽  
Riemannian Metrics ◽  
Ricci Solitons ◽  
Conformally Flat

Invariant Ricci solitons on three-dimensional metric Lie groups with semi-symmetric connection

2021 ◽  
pp. 80-85
Author(s):  
Pavel Nikolaevich Klepikov ◽  
◽  
Evgeny Dmitrievich Rodionov ◽  
Olesya Pavlovna Khromova ◽  
◽  
...  
Keyword(s):  
Lie Groups ◽  
Three Dimensional ◽  
Ricci Solitons ◽  
Symmetric Connection

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.

Algebraic Ricci solitons on metric Lie groups with zero Schouten–Weyl tensor

2017 ◽  
Vol 95 (1) ◽  
pp. 62-64
Author(s):  
P. N. Klepikov ◽  
E. D. Rodionov
Keyword(s):  
Lie Groups ◽  
Weyl Tensor ◽  
Ricci Solitons
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