Abstract
We consider η-Ricci solitons on Lorentzian para-Sasakian manifolds with Codazzi type of the Ricci tensor. Then we study η-Ricci solitons on ϕ-conformally semi-symmetric, ϕ-Ricci symmetric, and conformally Ricci semi-symmetric Lorentzian para-Sasakian manifolds. Finally, we construct an example of a three dimensional Lorentzian para-Sasakian manifold which admits η-Ricci solitons with non-constant scalar curvature.
Highlights
A Ricci soliton is a generalization of an Einstein metric
A contact metric manifold is said to be φ-conformally semi-symmetric if C · φ = 0, where C is the conformal curvature tensor
The paper is organized as follows: After preliminaries in Section 3, we study η-Ricci solitons on Lorentzian paraSasakian manifolds
Summary
A Riemannian or pseudo-Riemannian manifold (M, g), n ≥ 3, is said to be semi-symmetric if the curvature condition. A fundamental study on Riemannian semi-symmetric manifolds was introduced by Z. A contact metric manifold is said to be φ-conformally semi-symmetric if C · φ = 0, where C is the conformal curvature tensor. Motivated by the above studies, in the present paper we consider η-Ricci solitons on Lorentzian para-Sasakian manifolds with the curvature conditions C · φ = 0 and C · S = 0. Η-Ricci solitons on LP-Sasakian manifolds satisfying certain curvature conditions. We study η-Ricci solitons on φ-conformally semisymmetric LP-Sasakian manifolds. We construct an example of a three dimensional LP-Sasakian manifold which admits η-Ricci solitons with non-constant scalar curvature
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