Study of Certain New Tensors in a Finsler Space of Three-Dimensions

In one of his earlier papers in (1990), the author [7] has defined and studied several new tensors of second and third order. The author, further in Ref. [9] has defined and studied several properties of asymmetric third order new tensor Dijk, which is similar to the Cartan's torsion tensor [1], Cijk of a Finsler space of three dimensions. This tensor, however, satisfies Dijk li = 0, Dijk gjk = Di = D ni. Based on this tensor, author has defined several other tensors including Qijk = Dijk/0, similar to Pijk and D י ijkh similar to third curvature tensor Sijkh. The purpose of the present paper is to define and study a tensor Uijkkh, similar to second curvature tensor Pijkh and Vijkh similar to a very important tensor Tijkh, which was introduced independently by Kawaguchi [3] and Matsumoto [5] in (1972).