η-Ricci Solitons on α-Lorentzian Sasakian Manifolds">
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Kyungpook Mathematical Journal 2022; 62(4): 737-749

Published online December 31, 2022

Copyright © Kyungpook Mathematical Journal.

Some Geometric Properties of η-Ricci Solitons on α-Lorentzian Sasakian Manifolds

Shashikant Pandey and Abhishek Singh, Rajendra Prasad

Department of Mathematics and Astronomy, University of Lucknow, Lucknow, 226007 Uttar Pradesh, India
e-mail : shashi.royal.lko@gmail.com and lkoabhi27@gmail.com

Department of Mathematics and Astronomy, University of Lucknow, Lucknow, 226007 Uttar Pradesh, India
e-mail : rp.manpur@rediffmail.com

Received: December 20, 2021; Revised: April 19, 2022; Accepted: May 3, 2022

Abstract

We investigate the geometric properties of η-Ricci solitons on α-Lorentzian Sasakian (α-LS) manifolds, and show that a Ricci semisymmetric η-Ricci soliton on an α-LS manifold is an η-Einstein manifold. Further, we study φ-symmetric η-Ricci solitons on such manifolds. We prove that φ-Ricci symmetric η-Ricci solitons on an α-LS manifold are also η-Einstein manifolds and provide an example of a 3-dimensional α-LS manifold for the existence of such solitons.

Keywords: η*-Ricci solitons, φ*-Symmetric, Ricci semisymmetric, φ*Ricci symmetric, η* Einstein manifolds