This article is cited in 6 papers

Ricci solitons and gradient Ricci solitons on $N(k)$-paracontact manifolds

Uday Chand De^a, Krishanu Mandal<sup>b

a</sup> Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kol-700019, West Bengal, India
^b Department of Mathematics, K.K. Das College, GRH-17, Baishnabghata-Patuli, Kol-700084, West Bengal, India

Abstract: An $\eta$-Einstein paracontact manifold $M$ admits a Ricci soliton $(g,\xi)$ if and only if $M$ is a $K$-paracontact Einstein manifold provided one of the associated scalars $\alpha$ or $\beta$ is constant. Also we prove the non-existence of Ricci soliton in an $N(k)$-paracontact metric manifold $M$ whose potential vector field is the Reeb vector field $\xi$. Moreover, if the metric $g$ of an $N(k)$-paracontact metric manifold $M^{2n+1}$ is a gradient Ricci soliton, then either the manifold is locally isometric to a product of a flat $(n+1)$-dimensional manifold and an $n$-dimensional manifold of negative constant curvature equal to $-4$, or $M^{2n+1}$ is an Einstein manifold. Finally, an illustrative example is given.

Key words and phrases: paracontact manifold, $N(k)$-paracontact manifold, Ricci soliton, gradient Ricci soliton, Einstein manifold.

MSC: 53B30, 53C15, 53C25, 53C50, 53D10, 53D15.

Received: 14.02.2018
Revised: 01.06.2018

Language: English

DOI: 10.15407/mag15.03.307

Bibliographic databases:

• 
•