On Certain Special Vector Fields in a Finsler Space III On Certain Special Vector Fields in a Finsler Space III

Abstract

In an earlier paper in 2017, Rastogi and Bajpai[1] defined and studied a special vector field of the first kind in a Finsler space as follows:
Definition 1: A vector field Xi(x), in a Finsler space, is said to be a special vector field of the first kind, if (i) Xi/j = - δij and (ii) Xi hij = Ɵj, where Ɵj is a non-zero vector field in the given Finsler space.
In 2019, some more special vector fields in a Finsler space of two and three dimensions have been defined and studied by the authors Dwivedi et al.[2] and Dwivedi et al.[3] In Dwivedi et al.[3], the authors defined and studied six kinds of special vector fields in a Finsler space of three dimensions and, respectively, called them special vector fields of the second, third, fourth, fifth, sixth, and seventh kind. In the present paper, we shall study some curvature properties of special vector fields of the first and seventh kind in a Finsler space of three dimensions.