Keywords:-

Keywords: β-Kenmotsu manifolds, η-Ricci solitons, W_2- curvature tensor etc.

Article Content:-

Abstract

-Ricci solitons on Lorentzian - Kenmotsu manifold are considered an manifolds satisfying certain curvature Conditions, R(,X).S=0, S(,X).R=0, =0,.=0 We proved that in Lorentzian -Kenmotsu manifold (). Then the existence of an -Ricci solitons implies that M is Einstein manifold and if the Ricci curvature tensor satisfies, S(,X).R=0, then Ricci solitons  M is steady. If the condition =0, then =0, which shows that  is steady.

References:-

References

Ahmet, Y. De, U. C., Eftal, A. B. (2009): On Kenmotsu manifolds satisfying certain curvature conditions SUT, J. Math.45, no.2, 89-101.

Ahmet, Y. De U. C. (2010): On a type of Kenmotsu manifolds Differ. Geom. Dyn. Syst.12, 289-298.

Bagewadi, C. S. Prakasha D. G. and Basavarajappa, N. S. (2008): On Lorentzian β-Kenmotsu manifolds, Int. Jour. Math. Analysis, 19(2),919-927.

Ingalahalli, G. and Bagewadi, C. S. (2012): Ricci solitons α-Sasakian manifolds, ISRN Geometry, Vol. 2012, Article ID 421384, 13 Pages.

Bagewadi, C. S. and Kumar, E. G. (2004): Note on Trans- Sasakian manifolds, Tensor N. S. 65(1),80-88.

Baishya, K. K.(2017): Ricci Solitons in Sasakian manifold, Afrika Matimatika, 28,(7-8),1061-1066.

C. L. Bejan and M. Crasmareanu (2011): Ricci solitons in manifolds with quasi-contact curvature, Publ. Math. Debrecen, 78 (1), 235-243.

A. Bejancu and K. L. Duggal (1993): Real Hypersurface of indefinite Kahler manifolds, Int. Math. Sci., 16(3), 545-556.

Bejan, C. L., Crasmareanu, M.(2014) : Second order parallel tensor and Ricci solitons in 3-dimensional narmal Para-contact geometry, Anal. Global Anal. Geom. Doi: 10.1027/s/0455-014-9414-4.

Blaga, A. M. (2016): η-Ricci solitons on Lorentzian Para-Sasakian manifolds, Published by Faculty of Sciences and Mathematics, University of Nis, Serbia, filomat 30:2,(489-496).

Blaga, A. M. (2015): η-Ricci solitons on para-Kenmotsu manifolds, Balkan J. Geom. Appl., 20, 1-13.

Cao, H. D. (1996): Existence of gradient Kahler-Ricci Solitons, Elliptic and Parabolic methods in Geometry ( Minneapolis, M. N. (1-16).

Calin. C., Crasmareanu, M. (2010): From the Eisenhart Problem to the Ricci solitons in f-Kenmotsu manifold //Bull.Malays. Math.Soc.33.

Calin, C., Crasmareanu, M. (2012): Eta Ricci solitons on Hopf hyper surfaces in complex space forms, Revue Romaine de Mathematiques in complex space forms, Revue Romaine de Mathematiques Pures at appliqués Pures at appliqués 57,no. 1,55-63.

Calvaruso, G. and Perrone, D., (2014): Ricci Solitons in three-dimensional Paracontact geometry, arxiv: 1407.3458v1.

B. Y. Chen and S. Deshmukh (2014): Geometry of compact shrinking Ricci solitons, Balkan J. Geom. Appl.,19,13-31.

Cho, J. T., Kimura, M. (2009): Ricci solitons and real hyper-surfaces in a complex space form, Tohoku Math.J.61, No.2,205-212.

Chodosh, O. and F. T. H. Fong (2013): Rotational symmetry of conical Kahler- Ricci Solitons, arxiv:1304.0277v2.

Dragomir, S. and Ornea , L. (1998): Locally conformal Kaehler geometry, Progress in Mathemaics 155,Birkhauser Boston ,Inc., Boston, M.A.

Hamilton, R. S. (1988): Three Manifolds with positive Ricci curvature, J. Diff. Geom. 17,no. 2, 255-306.

Hamilton, R. S. (1993): Eaternal Solutions of The Ricci flow J. Diff., Geom.,38,1-11.

Matsumoto, K., Ianus, S. and Mihai, I. (1986): On P-Sasakian Manifold which Admit Certain Tensor fields, “ Publicationes Mathematicae Debrecen, Vol.33,pp.61-65.

Matsumotso, K. and Mihai, I. (1988): On a certain Transformation in a Lorenzian Para-Sasakian Manifold, Tensor N. S.Vol. 47, PP. 189-197.

Marrero, J. C. (1992): The Local structure of trans-Sasakian Manifolds, Ann. Mat. Pura Appl., 162 (4), 77-86.

Marrero, J. C. and. Chinea (1990): On trans-Sasakian manifolds, Proceedings of the Xivth Spanish-Portuquese conferences on Mathematics, Vol. I-III (spanish) (Puerto da Lacruz, 659, Univ. La Laguna, La Laguna.)

H. G. Nagaraja and C. R. Premalatha (2012): Ricci solitons in Kenmotsu manifolds, Journal of Mathematical Analysis, 3, 18-24.

S. K. Pandey, G. Pandey, K. Tiwari and R. N. Singh (2014): On a semi-symmetric non-metric connection in an indefinite para Sasakian manifolds ,Journal of Mathematics and Computer Sciences 12,159-172.

R. L. Patel S. K. Pandey and R. N. Singh (2018): Ricci Solitons on (ε)-Para Sasakian manifolds International journal of Mathematics And its Applications 6, (1-A), 73-82.

R. L. Patel S. K. Pandey and R. N. Singh (2018): On Ricci Solitons in (ε)-Kenmotsu manifolds International Journal of Engineering Sciences and Management Research, 5, (2),17-23.

Perelman, G. (2003): Ricci flow with surgery on three Manifolds, http://ar Xiv.org/abs Math 0303109,1-22.

Pokhariyal, G.P. (1982): study of a new curvature tensor in Sasakian Manifold.”Tensor N.S. Vol.36, No.2, pp.222-225.

R. Sharma (2008): Certain results on K-contact and ( k,μ)-contact manifolds, Journal of Geometry, 89 (1-2), 138-147.

Sesum, N. Limiting behariour of Ricci flow, arxiv: DG. Math. DG/0402194.

Shaikh, A. A. De, U. C. Binh. T. Q. (2001): On K-contact η-Einstein manifolds. Steps in differential Geometry (Debrecen 2000), Inst. Math. Inform. Debrecen 311-315.

R. N. Singh, S. K. Pandey, G. Pandey and K. Tiwari (2014): On a semi-symmetric metric connection in an (ε)-Kenmotsu manifold, Commun. Korean Math. Soc., 29 (2), 331-343.

Tanno, S. (1969): The Automorphism Groups of Almost contact Riemannian Manifolds “ Tohoku Mathematical Sournal Vol. 21, No.1, pp.21-38 doi:10.2748/tmj/1178243031.

Yildiz, A. and Murathan, C. (2005): “On Lorentzian α-Sasakian Manifolds,” Kyungpook Mathematical Journal, Vol.45, No.1, pp. 95-103.

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Singh, R. N., & Patel, R. L. (2023). η-Ricci solitons on Lorentzian β-Kenmotsu manifold. International Journal Of Mathematics And Computer Research, 11(5), 3410-3415. https://doi.org/10.47191/ijmcr/v11i5.03