The objective of this paper is to deal with Kenmotsu manifolds admitting [Formula: see text]-Ricci-Yamabe solitons. First, it is proved that if a Kenmotsu manifold [Formula: see text] which admits an [Formula: see text]-Ricci-Yamabe soliton, then the manifold [Formula: see text] is Einstein and is of constant scalar curvature. Then, some important characterizations, which classify Kenmotsu manifolds admitting such solitons, are obtained and an example given which supports our results.

In the present paper, we deal with the generic submanifold admitting a Ricci soliton in Sasakian manifold endowed with concurrent vector …eld. Here, we …nd that there exists never any concurrent vector …eld on the invariant distribution D of generic submanifold M. Also, we provide a necessary and su¢ cient condition for which the invariant distribution D and anti-invariant distribution D ? of M are Einstein. Finally, we give a characterization for a generic submanifold of Sasakian manifold to be a gradient Ricci soliton.

In this paper, we deal with the geometric properties of cosymplectic manifold. We give some classifications for a cosymplectic manifold endowed with some special vector fields, such as contact, concircular, recurrent, torse-forming and some characterizations for such a manifold admitting a Ricci soliton given as to be Einstein, η−Einstein, almost quasi-Einstein and nearly quasi-Einstein.

In this paper, we consider the submanifold M of a Kenmotsu manifoldM endowed with torqued vector field T. Also, we study the submanifold M admitting a Ricci soliton of both Kenmotsu manifoldM and Kenmotsu space formM (c). Indeed, we provide some necessary conditions for which such a submanifold M is an η−Einstein. We have presented some related results and classified. Finally, we obtain an important characterization which classifies the submanifold M admitting a Ricci soliton of Kenmotsu space formM (c).