On the Existence of Concurrent Vector Fields in a Finsler Space-II

In (1978) Singh [10] studied concurrent vector fields using Berwald's covariant derivative instead of Carton and proved that A vector field on is concurrent in the Berwald's sense if and only if it is concurrent in the Cartan's sense. It is interesting to note that apparently there seems to be no difficulty in taking Berwald's covariant derivative in Definition 1.1, but after some analysis it is found that this is not true. The purpose of the present paper is to study the existence of concurrent vector fields using Berwald's covariant derivative and to give an alternative definition of vector fields which we shall call B-concurrent. Some properties of concurrent, P-concurrent and B-concurrent vector fields in a Finsler space have also been studied in this paper.