CONFORMAL AND PARACONTACTLY GEODESIC TRANSFORMATIONS OF ALMOST PARACONTACT METRIC STRUCTURES

Abstract

We give the expressions of the virtual and the structure tensor fields of an almost paracontact metric structure. We also introducethe notion of paracontactly geodesic transformation and prove thatthe structure tensor field is invariant under conformal andparacontactly geodesic transformations. For the particular case of para-Kenmotsu structure, we give a necessary and sufficient condition for a conformal transformation to map it to an $\alpha$-para-Kenmotsu structure and show that a para-Kenmotsu manifold admits no nontrivial paracontactly geodesic transformation of the metric. In the conformal case, the virtual tensor field is invariant.