$\left(LCS\right)_{n}-$Manifolds Admitting Almost $\eta-$Ricci Solitons on Some Special Curvature Tensors
Abstract
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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References
A.A. Shaikh, On Lorentzian almost paracontact manifolds with a structure of the concircular type, Kyungpook Math. J. 43 (2003), 305-314.
A.A. Shaikh and H. Ahmad, Some transformations on $left(LCSright)_{n}$ manifolds, Tsukuba J. Math. 38 (2014), 1-24. https://doi.org/10.21099/tkbjm/1407938669
C.A. Mantica and L.G. Molinari, A note on concircular structure spacetimes, Commun. Korean Math. Soc. 34(2) (2019), 633-635.
A.A. Shaikh and T.Q. Binh, On weakly symmetric $left(LCSright) _{n}$ manifolds, J. Adv. Math. Stud. 2 (2009), 75-90.
A.A. Shaikh, T. Basu and S. Eyasmin, On the existence of $Phi-$recurrent $left(LCSright)_{n}$ manifolds, Extracta Math. 23 (2008), 71-83.
A.A. Shaikh and S.K. Hui, On generalized $Phi-$recurrent $left(LCSright)_{n}$ manifolds, AIP Conf. Proc. 1309 (2010), 419-429. https://doi.org/10.1063/1.3525143
A.A. Shaikh, Y. Matsuyama and S.K. Hui, On invariant submanifolds of $left(LCSright)_{n}$ manifolds, J.Egyptian Math. Soc. 24 (2016), 263-269. https://doi.org/10.1016/j.joems.2015.05.008
A.A. Shaikh, B.R. Datta, A. Ali and A.H. Alkhaldi, (LCS) manifolds and Ricci solitons, Int. J. Geom. Methods Mod. Phys. 18(09) (2021), 2150138. https://doi.org/10.1142/s0219887821501383
K.K. Baishy, More on $eta-$Ricci Solitons in $left(LCSright)_{n}-$Manifolds, Bulletin of the Transilvabia University of Braşov. 11(60) (2018), No.1.
M. Atçeken, Ü. Yıldırım and S. Dirik, Pseudoparallel invariant submanifolds of $left(LCSright)_{n}-$manifolds, Korean J. Math. 28(2) (2020), 275-284.
S.K. Hui, R.C. Lemence and D. Chakraborty, Ricci solitons on Ricci Pseudosymmetric $left(LCSright)_{n}-$manifolds, Honam Mathematical J. 40(2) (2018), 325-346.
A.A. Shaikh, Some results on $left(LCSright)_{n}-$manifolds, J. Korean Math. Soc. 46(33) (2009), 449-461.
R.S. Hamilton, Three manifolds with positive Ricci curvature, J. Differential Geom. 17(2) (1982), 255-306. https://doi.org/10.4310/jdg/1214436922
J.T. Cho and M. Kimura, Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math. J. 61(2) (2009), 205-212. https://doi.org/10.2748/tmj/1245849443
C. Calin and M. Crasmareanu, $eta-$Ricci solitons on Hopf hypersurfaces in complex space forms, Revue Roumainede Mathematiques pureatappliques 57(1) (2021), 55-63.
R. Sharma, Certain results on $k-$contact and $left( kappa,muright) -$contact manifolds, J. of Geom. 89 (2008), 138-147. https://doi.org/10.1007/s00022-008-2004-5
R. Deszcz, On Ricci-pseudosymmetric warped products, Demonstratio Math. 22 (1989), 1053-1065. https://doi.org/10.1515/dema-1989-0411
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