The object of the present paper is to investigate the nature of Ricci solitons on D-homothetically deformed Kenmotsu manifold with generalized weakly symmetric and generalized weakly Ricci symmetric curvature restrictions.
( C S ) 4 -spacetimes with Einstein field equations under some curvature restriction named generalized weakly Ricci-symmetry have been studied. We have proved that if the characteristic vector field ξ of a generalized weakly Ricci-symmetric ( C S ) 4 -spacetime obeying Einstein equation is a Killing vector field, then such a spacetime admits (i) curvature collineation, (ii) conformal...
Recently the present author introduced the notion of generalized quasi-conformal curvature tensor which bridges conformal curvature tensor, concircular curvature tensor, projective curvature tensor and conharmonic curvature tensor. The object of the present paper is to find out curvature conditions for which Ricci solitons in Sasakian manifolds are sometimes shrinking and some other time remain expanding.
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