Ricci Solitons on Nearly Kenmotsu Manifolds with Semi-symmetric Metric Connection

Year 2019, Volume: 4 Issue: 3, 131 - 140, 31.12.2019

Gülhan Ayar Dilek Demirhan

https://doi.org/10.30931/jetas.643643

Cited By: 5

Abstract

In this work, we give some basic informations about Ricci solitons on a nearly Kenmotsu manifold and some structures on this manifolds satisfying semi-symmetric metric connection. And then we consider some important results and theorems of Ricci solitons on Ricci-recurrent and Φ-recurrent nearly Kenmotsu manifolds with semi-symmetric metric connection. Also final part of the present paper, we study Ricci solitons on quasi-projectively flat nearly Kenmotsu manifolds with semi-symmetric metric connection.

Keywords

Nearly Kenmotsu manifold, Ricci soliton, Semi-symmetric metric connection

References

• Bejan, C.L., Crasmareanu, M., “Second order parallel tensors and Ricci solitons in 3-dimensional normal paracontact geometry”, Ann. Glob. Anal. Geom. (2014), doi:10. 1007/s10455-014-9414-4. Hamilton, R.S., “Three manifolds with positive Ricci curvature”, Journal of Differential Geometry 17 (2) (1982) : 225-306.
• Hamilton, R.S., “The Ricci flow on surfaces”, Contemporary Mathematics 71 (1988) : 237-261.
• Hamilton, R.S., “The Ricci flow on surfaces. In: Mathematics and general relativity (Santa Cruz, CA, 1986)”, Contemp. Math. Amr. Math. Soc., Providence 71 (1988) : 237-262.
• Nagaraja, H.G., Venu, K., “Ricci Solitons in Kenmotsu Manifold”, Journal of Informatics and Mathematical Sciences 8 (2016) : 29.
• Oztürk, H., “On α−Kenmotsu manifolds satisfying semi-symmetric conditions”, Konuralp Journal of Mathematics 5 (2017) : 192-193.
• Kenmotsu, K., “A class of contact Riemannian manifold”, Tohoko Math. J. 24 (1972) : 93-103.
• Nomizu, K., “On hypersurfaces satisfying a certain condition on the curvature tensor”, Tohoko Mat. J. 20 (1968) : 46-69.
• Blair, D.E., “Contact manifolds in Riemannian geometry”, Lecture Notes in Mathematics 509 (1976), Springer-Verlag, Berlin.
• Shukla, A., “Nearly trans-Sasakian manifolds”, Kuwait J. Sci. Eng. 23 (2) (1996) : 139–144.
• Küpeli Erken, I., Piotr D., Murathan, C., “On the existence of proper nearly Kenmotsu manifolds”, Mediterr. J. Math. 13 (2016) : 4497-4507.
• Prasad, R., Kumar, S., Gautam, U.K., “On nearly Kenmotsu manifolds with semi-symmetric metric connection”, Ganita 68 (1) (2018) : 133.
• De, U.C., “On ϕ−recurrent Kenmotsu manifolds”, Turk J. Math. 33 (2009) : 17-25.
• Ayar, G., Yıldırım, M., “η-Ricci solitons on nearly Kenmotsu manifolds”, Asian-European Journal of Mathematics 12 (6) (2019) : 2040002.
• Ayar, G., Yıldırım M., “Ricci solitons and gradient Ricci solitons on nearly Kenmotsu manifolds”, Facta Universitatis (NIS) Ser. Math. Inform. 34 (3) (2019) : 503-510.