Certain results on generalized $${\varvec{(k,\,\mu )}}$$ ( k , μ ) -contact metric manifolds

Abstract

The object of the present paper is to study second order symmetric parallel tensors in generalized \((k,\,\mu )\)-contact metric manifolds and its applications to Ricci solitons. Next, we prove that a generalized \((k,\,\mu )\)-contact metric manifold M admits a Ricci soliton whose potential vector field is the Reeb vector field \(\xi \) if and only if M is a Sasaki–Einstein manifold. Finally, we give some examples of generalized \((k,\,\mu )\)-contact metric manifold.