Torse forming vector fields and exterior concurrent vector fields on Riemannian manifolds and applications

Abstract

We interrelate the concept of a torse forming vector field and the concepts of exterior concurrent and quasi-exterior concurrent vector fields. Different second order properties of a torse forming vector field T are studied, as for instance it is proved that any torse forming is a quasi-exterior concurrent vector field. We obtain a necessary and sufficient condition for a torse forming vector field to be 2-exterior concurrent. In this case a foliation is given.Some applications of the existence of torse formings on Sasakian manifolds and Kenmotsu manifolds, respectively, are discussed.