Kenmotsu manifold admitting Shouten-van-Kampen connection

Abstract

 In this paper we study Schouten-Van Kampen connection associated to Kenmotsu manifold with metric g as an almost Ricci soliton. Firstly, we prove that if potential vector field of almost Ricci soliton is point wise collinear with Reeb vector field ξ, then it reduces to a homothetic vector field and if this homothetic vector field is Killing, then almost Ricci soliton reduces to steady Ricci soliton. Next we prove that the potential vector field of an almost Ricci soliton preserves Reeb vector field ξ, contact form η and (1,1) tensor φ. Finally, we study geometric properties of torse forming and concircular vector fields on a Kenmotsu manifold.