Generalized Ricci solitons on contact metric manifolds

In the present paper we prove that, if a N ( k )-contact manifold of dimension ( 2 n + 1 ) satisfies the generalized Ricci soliton equation ( 1.4 ) and X = g r a d f , f being a smooth function, then f is a constant function. Furthermore, if c 2 ≠ 0 , then the manifold is either locally isometric to the product E n + 1 ( 0 ) × S n ( 4 ) for n > 1 and flat for n = 1 , or the manifold is an Einstein one.