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http://dx.doi.org/10.5666/KMJ.2019.59.3.537

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

Siddiqi, Mohd Danish (Department of Mathematics, Jazan University, Faculty of Science)
Publication Information
Kyungpook Mathematical Journal / v.59, no.3, 2019 , pp. 537-562 More about this Journal
Abstract
The aim of the present paper is to study the ${\delta}$-Lorentzian trans-Sasakian manifold endowed with semi-symmetric metric connections admitting ${\eta}$-Ricci Solitons and Ricci Solitons. We find expressions for the curvature tensor, the Ricci curvature tensor and the scalar curvature tensor of ${\delta}$-Lorentzian trans-Sasakian manifolds with a semisymmetric-metric connection. Also, we discuses some results on quasi-projectively flat and ${\phi}$-projectively flat manifolds endowed with a semi-symmetric-metric connection. It is shown that the manifold satisfying ${\bar{R}}.{\bar{S}}=0$, ${\bar{P}}.{\bar{S}}=0$ is an ${\eta}$-Einstein manifold. Moreover, we obtain the conditions for the ${\delta}$-Lorentzian trans-Sasakian manifolds with a semisymmetric-metric connection to be conformally flat and ${\xi}$-conformally flat.
Keywords
${\eta}$-Ricci Solitons; ${\delta}$-Lorentzian trans-Sasakian manifold; semi-symmetric metric connection; curvature tensors; Einstein manifold;
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Times Cited By KSCI : 1  (Citation Analysis)
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