ON GENERIC SUBMANIFOLD OF SASAKIAN MANIFOLD WITH CONCURRENT VECTOR FIELD

Abstract

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