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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)
  • Received : 2018.02.14
  • Accepted : 2018.10.02
  • Published : 2019.09.23

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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