Certain Results on Almost Kenmotsu $(\kappa ,\mu ,\nu)-$Spaces

Abstract

The present paper deals with the study of Ricci soliton on weak symmetries of almost Kenmotsu $(\kappa ,\mu ,\nu)-$space and its geometric properties. Also, we obtain the condition for Ricci soliton on weakly symmetric and weakly Ricci symmetric almost Kenmotsu $(\kappa ,\mu ,\nu)-$space with the tensor field ${\rm \pounds }_{\xi }g +2S$ is parallel to be shrinking, steady and expanding respectively.