On the Existence of Semi-Parallel Vector Fields in a Finsler Space

This paper is concerned with the existence of semi parallel vector field in a Finsler space. Semi paralleled vector field in a Riemannian manifold was studied by C.M. Fulton and M. Hashiguchi, while semi parallel vector field and normalized semi parallel vector field in a Finsler space were defined and studied by Singh and Prasad. In this chapter while studying the existence of semi parallel vector field and normalized semi parallel vector field analogous to the study of the existence of concurrent vector field, it has also been shown that the definition given by Singh and Prasad, of semi parallel vector field and normalized semi parallel vector field. In a Finsler space in its present form is untenable. We have given a modified definition of semi-parallel vector field and normalized semi-parallel vector field in a Finsler space and studied some of their properties vis-a-vis other will know as Finsler space such as C2-like, P2-like, C-reducible, R-reducible, P-reducible and S3-like etc.