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

Arpan Sardar; Uday Chand De;


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.

Vol. 24 (2023), No. 3, pp. 1515-1525
DOI: 10.18514/MMN.2023.4098

Download: MMN-4098