Generalized Ricci Solitons on K-contact manifolds

Year 2020, Volume: 8 Issue: 2, 165 - 169, 15.10.2020

Gopal Ghosh U.c. De

https://doi.org/10.36753/mathenot.683478

Cited By: 2

Abstract

The object of the present paper is to study K-contact manifold admitting generalised Ricci solitons. We prove that a $K$-contact manifold of dimension $(2n+1)$ satisfying the generalised Ricci soliton equation is an Einstein one. Finally, we obtain several remarks.

....................................................................................

.............................................................................

...............................................................

..............................................................

Keywords

$ K$-contact manifold, Generalised Ricci soliton, Einstein manifold

References

• Blair, D.E., Contact manifolds in Reimannian geometry, Lecture notes in Math. 509, Springer-Verlag., 1976.
• Boyer, C.P., Galicki, K., Einstein manifold and contact geometry. Proc. Amer. Math. Soc., 129 (2001), 2419-2430.
• Chrusciel, P. T., Reall, H. S., Tod, P., On non-existence of static vacuum black holes with degenerate components of the event horizon, Classical Quantum Gravity, 23 (2006), 549-554.
• Deshmukh, S., Aloden, H., A note on Ricci soliton, Balkan J. of Geom. and Appl., 16 (2011), 48-55.
• Deshmukh, S., Jacobi-type vector fields on Ricci solitons, Bull. Mathematique de la societe des sciences Mathematiques de Roumanie Nouvelle Series., 103 (2012), 41-50.
• De, U.C. and Biswas, S., On K-contact eta-Einstein manifolds. Bull. Soc. Math., 16 (1990), 23-28.
• De, U.C., De, A., On some curvature properties of K-contact manifolds. Extracta Math., 27 (2012), 125-134.
• Guha, N. and De, U.C., On K-contact manifolds. Serdica-Bulgaricae Math. Publ., 19 (1993), 267-272.
• Jezierski, J., On the existance of Kundts metrics and degenerate (or extremal) Killing horizones, , Classical Quantum Gravity, 26(2009), 035011, 11pp.
• Jun, J. B., Kim, U. K., On 3-dimensional almost contact metric manifolds, Kyungpook Math. J., 34(1994), 293-301.
• Koufogiorgos, T., Contact metric manifolds. Ann. Global Anal. Geom., 11 (1993), 25-34.
• Mekki, M. E., Cherif, A. M., Generalised Ricci solitons on Sasakian manifolds, Kyungpook Math. J., 57 (2017)677-682.
• Nurowski. P., Randall, M., Generalised Ricci solitons, J Geom. Anal., 26(2016), 1280-1345.
• Prasad, R., Srivastava, V., On phi-symmetric K-contact manifolds. IJRRAS, 16 (2013), 104-110.
• Sasaki, S., Lecture notes on almost contact manifolds, Part I. Tohoku Univ., $(1965)$.
• Tarafdar, D. and De, U.C., On K-contact manifolds. Bull. Math. de la Soc. Sci. Math de Roumanie, 37 (1993), 207-215.
• Yano, K. and Kon, M., Structures on manifolds. Vol 40, World Scientific Press, 1989.
• Yildiz, A. and Ata, E., On a type of K-contact manifolds. Hacettepe J. Math. Stat., 41 (2012), 567-571.