Almost $\eta-$Ricci Solitons on Pseudosymmetric Lorentz Sasakian Space Forms

Year 2023, Volume: 6 Issue: 1, 44 - 59, 31.03.2023

Tuğba Mert , Mehmet Atçeken

https://doi.org/10.33434/cams.1236095

Cited By: 1

Abstract

In this paper, we consider pseudosymmetric Lorentz Sasakian space forms admitting almost $\eta-$Ricci solitons in some curvature tensors. Ricci pseudosymmetry concepts of Lorentz Sasakian space forms admits $\eta-$Ricci soliton have introduced according to the choice of some special curvature tensors such as Riemann, concircular, projective, $\mathcal{M-}$projective, $W_{1}$ and $W_{2}.$ Then, again according to the choice of the curvature tensor, necessary conditions are given for Lorentz Sasakian space form admits $\eta-$Ricci soliton to be Ricci semisymmetric. Then some characterizations are obtained and some classifications have made under the some conditions.

Keywords

Ricci-pseudosymmetric Manifold , η-Ricci Soliton , Lorentz Sasakian Space Form

References

• [1] G. Perelman, The entropy formula for the Ricci flow and its geometric applications, http://arXiv.org/abs/math/0211159, (2002), 1–39.
• [2] G. Perelman, Ricci flow with surgery on three manifolds, http://arXiv.org/abs/math/0303109, (2003), 1–22.
• [3] R. Sharma, Certain results on k-contact and (k,μ)-contact manifolds, J. Geom., 89 (2008),138–147.
• [4] S.R. Ashoka, C.S. Bagewadi, G. Ingalahalli, Certain results on Ricci Solitons in α−Sasakian manifolds, Hindawi Publ. Corporation, Geometry, Vol.(2013), Article ID 573925,4 Pages.
• [5] S.R. Ashoka, C.S. Bagewadi, G. Ingalahalli, A geometry on Ricci solitons in (LCS)n manifolds, Diff. Geom.-Dynamical Systems, 16 (2014), 50–62.
• [6] C.S. Bagewadi, G. Ingalahalli, Ricci solitons in Lorentzian-Sasakian manifolds, Acta Math. Acad. Paeda. Nyire., 28 (2012), 59-68.
• [7] G. Ingalahalli, C. S. Bagewadi, Ricci solitons in α−Sasakian manifolds, ISRN Geometry, Vol.(2012), Article ID 421384, 13 Pages.
• [8] C.L. Bejan, M. Crasmareanu, Ricci Solitons in manifolds with quasi-contact curvature, Publ. Math. Debrecen, 78 (2011), 235-243.
• [9] A. M. Blaga, η−Ricci solitons on para-kenmotsu manifolds, Balkan J. Geom. Appl., 20 (2015), 1–13.
• [10] S. Chandra, S.K. Hui, A. A. Shaikh, Second order parallel tensors and Ricci solitons on (LCS)n-manifolds, Commun. Korean Math. Soc., 30 (2015), 123–130.
• [11] B.Y. Chen, S. Deshmukh, Geometry of compact shrinking Ricci solitons, Balkan J. Geom. Appl., 19 (2014), 13–21.
• [12] S. Deshmukh, H. Al-Sodais, H. Alodan, A note on Ricci solitons, Balkan J. Geom. Appl.,16 (2011), 48–55.
• [13] C. He, M. Zhu, Ricci solitons on Sasakian manifolds, arxiv:1109.4407V2, [Math DG], (2011).
• [14] M. Atc ̧eken, T. Mert, P. Uygun, Ricci-Pseudosymmetric (LCS) −manifolds admitting almost η−Ricci solitons, Asian J. n Math. Comput. Research, 29(2), 23-32,2022.
• [15] H. Nagaraja, C. R. Premalatta, Ricci solitons in Kenmotsu manifolds, J. Math. Analysis, 3(2) (2012), 18–24.
• [16] M. M. Tripathi, Ricci solitons in contact metric manifolds, arxiv:0801,4221 V1, [Math DG], (2008).
• [17] D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Volume 203 of Progress in Mathematics, Birkhauser Boston, Inc., Boston, MA, USA, 2nd edition, 2010.
• [18] P. Alegre, D. E. Blair, A. Carriazo, Generalized Sasakian space form, Israel J. Math., 141 (2004), 157-183.
• [19] P. Alegre, A. Carriazo, Semi-Riemannian generalized Sasakian space forms, Bulletin of the Malaysian Math. Sci. Soc., 41(1) (2018), 1–14.
• [20] J.T. Cho, M. Kimura, Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math. J, 61(2) (2009), 205-212.
• [21] G. Ayar, M. Yıldırım, η−Ricci solitons on nearly Kenmotsu manifolds, Asian-European J. Math., 12(6), 2040002 (2019).
• [22] G. Ayar, M. Yıldırım, Ricci solitons and gradient Ricci solitons on nearly Kenmotsu manifolds, Facta Universitatis, Series: Mathematics and Informatics, (2019), 503-510.
• [23] M.Yıldırım, G. Ayar, Ricci solitons and gradient Ricci solitons on nearly Cosymplectic manifolds, J. Univers. Math., 4(2) (2021), 201-208.
• [24] G. Ayar, D. Dilek, Ricci Solitons on Nearly Kenmotsu Manifolds with Semi-symmetric Metric Connection, Journal of Engineering Technology and Applied Sciences, 4(3) (2019), 131-140.
• [25]G. Ayar, Kenmotsu manifoldlarda konformal ricci solitonlar, Afyon Kocatepe Universitesi Fen Ve Mu ̈hendislik Bilimleri Dergisi 19(3) (2019), 635-642. [26] M. Turan, C. Yetim, S.K. Chaubey, On quasi-Sasakian 3-manifolds admitting η−Ricci solitons, Filomat, 33(15) (2019), 4923–4930.
• [27] G. Ayar, S. K. Chaubey, M-projective curvature tensor over cosymplectic manifolds, Differ. Geom. Dyn. Syst., 21 (2019), 23-33.
• [28] G. Ayar, H.R Cavusoglu, Conharmonic curvature tensor on nearly cosymplectic manifolds with generalized tanaka-webster connection, Sigma J. Eng. Nat. Sci, 39(5) (2021), 9-13.
• [29] G. Ayar, Pseudo-projective and quasi-conformal curvature tensors on Riemannian submersions, Math. Meth. App. Sci., 44(17), 13791-13798.
• [30] G. Ayar, Some curvature tensor relations on nearly cosymplectic manifolds with Tanaka-Webster Connection, Univers. J. Math. Appl., 5(1) (2022), 24-31.
• [31] S.K. Chaubey, R. H. Ojha,On the m-projective curvature tensor of a Kenmotsu manifold, Differ. Geom. Dyn. Syst., 12(2010), 52-60.
• [32] S. K Chaubey ,S. Prakash, R Nivas, Some Properties of M-projective curvature tensor m- in Kenmotsu manifolds, Bulletin of Mathematical Analysis and Applications, 4(3) (2012), 48-56.