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KYUNGPOOK Math. J. 2019; 59(3): 537-562

Published online September 23, 2019

Copyright © Kyungpook Mathematical Journal.

η-Ricci Solitons in δ-Lorentzian Trans Sasakian Manifolds with a Semi-symmetric Metric Connection

Mohd Danish Siddiqi

Department of Mathematics, Jazan University, Faculty of Science, Jazan, Kingdom of Saudi Arabia
e-mails : anallintegral@gmail.com, msiddiqi@jazanu.edu.sa

Received: February 14, 2018; Revised: August 29, 2018; Accepted: October 2, 2018

Abstract

The aim of the present paper is to study the δ-Lorentzian trans-Sasakian manifold endowed with semi-symmetric metric connections admitting η-Ricci Solitons and Ricci Solitons. We find expressions for the curvature tensor, the Ricci curvature tensor and the scalar curvature tensor of δ-Lorentzian trans-Sasakian manifolds with a semi-symmetric-metric connection. Also, we discuses some results on quasi-projectively flat and ϕ-projectively flat manifolds endowed with a semi-symmetric-metric connection. It is shown that the manifold satisfying R̄.S̄ = 0, P̄.S̄ = 0 is an η-Einstein manifold. More-over, we obtain the conditions for the δ-Lorentzian trans-Sasakian manifolds with a semi-symmetric-metric connection to be conformally flat and ξ-conformally flat.

Keywords: η-Ricci Solitons, δ-Lorentzian trans-Sasakian manifold, semi-symmetric metric connection, curvature tensors, Einstein manifold.