$\left(LCS\right)_{n}-$Manifolds Admitting Almost $\eta-$Ricci Solitons on Some Special Curvature Tensors

  • Tuğba Mert Department of Mathematics, University of Sivas Cumhuriyet, 58140, Sivas, Turkey
  • Mehmet Atçeken Department of Mathematics, University of Aksaray, 68100, Aksaray, Turkey
  • Pakize Uygun Department of Mathematics, University of Aksaray, 68100, Aksaray, Turkey
  • Shashikant Pandey Department of Mathematics and Astronomy, University of Lucknow, India
Keywords: $\left(LCS\right)_{n}-$manifold, Ricci-pseudosymmetric manifold, $\eta-$Ricci soliton


In this paper, we consider $\left(LCS\right)_{n}$ manifold admitting almost $\eta-$Ricci solitons by means of curvature tensors. Ricci pseudosymmetry concepts of $\left(LCS\right)_{n}$ manifold admitting $\eta-$Ricci soliton have introduced according to the choice of some special curvature tensors such as pseudo-projective, $W_{1}$, $W_{1}^{\ast}$ and $W_{2}.$ Then, again according to the choice of the curvature tensor, necessary conditions are searched for $\left(LCS\right)_{n}$ manifold admitting $\eta-$Ricci soliton to be Ricci semisymmetric. Then some characterizations are obtained and some classifications have made.


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How to Cite
Mert, T., Atçeken, M., Uygun, P., & Pandey, S. (2023). $\left(LCS\right)_{n}-$Manifolds Admitting Almost $\eta-$Ricci Solitons on Some Special Curvature Tensors. Earthline Journal of Mathematical Sciences, 13(2), 291-311. https://doi.org/10.34198/ejms.13223.291311