Certain Results on N(k)- Contact Metric Manifolds and Torse-Forming Vector Fields

In this paper, we study N(k)-contact metric manifolds endowed with a torse-forming vector field and give some characterizations for such manifolds. Then, we deal with N(k)-contact metric manifolds admitting a Ricci soliton and find that the potential vector field V of the Ricci soliton is a constant multiple of E. Also, we obtain a necessary condition for a torse-forming vector field to be recurrent and Killing on M.