D-Concurrent Vector Field In a Finsler Space of Three-Dimensions

Concurrent vector fields in a Finsler space were first of all defined and studied by Tachibana [9] in 1950, followed by Matsumoto and Eguchi [2] and others. In 2004, Rastogi and Dwivedi [4] studied the existence of concurrent vector fields in a Finsler space of n-dimensions and showed that the definition of concurrent vector fields in its present form is unsuitable. Further, they modified the definition of concurrent vector fields in a Finsler space of n-dimensions. Recently, Rastogi [6], defined and studied weakly and partially concurrent vector fields in a Finsler space of three-dimensions. The purpose of the present paper is to define and study a vector field Xi(x) in F3, called D-concurrent vector field, which is based on a tensor Dijk defined and studied by Rastogi [5,7]. We have also defined and studied weakly and partially Dconcurrent vector fields of various types and relationship between them.