$N(\kappa)$-contact Riemann solitons with certain potential vector fields

Abstract

In the present article we find the nature of $N(\kappa)$-contact metric manifolds admitting Riemann solitons with some restrictions on the potential vector fields. The cases, when the potential vector field is collinear with the Reeb vector field and when it is infinitesimal contact transformation are specially treated. Moreover, it is proved that if the potential vector field is a gradient vector field, then the manifold considered is isometric to a product manifold. The validity of the obtained results are ensured with two non-trivial examples.