Affiliation:
1. Department of Mathematics , Pachhunga University College , Mizoram , India
Abstract
Abstract
The object of the present paper is to study Ricci soliton in β-Kenmotsu manifolds. Here it is proved that a symmetric parallel second order covariant tensor in a β-Kenmotsu manifold is a constant multiple of the metric tensor. Using this result, it is shown that if (ℒVg +2S)is ∇-parallel where V is a given vector field, then the structure (g, V, λ) yields a Ricci soliton. Further, by virtue of this result, we found the conditions of Ricci soliton in β-Kenmotsu manifold to be shrinking, steady and expending respectively. Next, Ricci soliton for 3-dimensional β-Kenmotsu manifold are discussed with an example.
Reference34 articles.
1. [1] A. Futaki, H. Ono, and G. Wang, Transverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds, J. Diff. Geom, 83/3, (2009), 585–636
2. [2] A. Ghosh, R. Sharma, and J. T. Cho, Contact metric manifolds with η-parallel torsion tensor, Ann. Glob. Anal. Geom., 34, (2008), 287–299
3. [3] A. M. Blaga, Eta-Ricci soliton on para-Kenmotsu manifold, Balkan Journal of Geometry and Its Applications, 20/1, (2015), 1–31
4. [4] B. Barua and U. C. De, Characterizations of a Riemannian manifold admitting Ricci solitons, Facta Universitatis(NIS)Ser. Math. Inform, 28/2, (2013), 127–132
5. [5] B. Chow, Peng Lu, and Lei Ni, Hamiltons Ricci flow, AMS Science Press, 77, (2006)