Conformal vector fields on N(k)-paracontact and para-Kenmotsu manifolds

Abstract

. In this article, we initiate the study of conformal vector fields in paracontact geometry. First, we establish that if the Reeb vector field ζ is a conformal vector field on N ( k ) -paracontact metric manifold, then the manifold becomes a para-Sasakian manifold. Next, we show that if the conformal vector field V is pointwise collinear with the Reeb vector field ζ , then the manifold recovers a para-Sasakian manifold as well as V is a constant multiple of ζ . Furthermore, we prove that if a 3-dimensional N ( k ) -paracontact metric manifold admits a Killing vector field V , then either it is a space of constant sectional curvature k or, V is an infinitesimal strict paracontact transformation. Besides these, we also investigate conformal vector fields on para-Kenmotsu manifolds.