On D-homothetically deformed N(k)-contact metric manifolds

Abstract

In the present paper, we have studied generalized weakly symmetric and generalized weakly Ricci symmetric D-homothetically deformed N(k)-contact metric manifolds. Also we have studied Ricci solitons on deformed N(k)-contact metric manifold and obtained several results if the manifold has generalized weakly symmetric and generalized weakly Ricci symmetric restrictions. We have also proved that there does not exist a Ricci soliton in a D-homothetically deformed N(k )-contact metric manifold. Finally, we give an example.