On Some New Tensors and their Properties in A Five-Dimensional Finsler Space-III

Berwald [1, 2] developed the study of two-dimensional Finsler spaces, whose idea was followed by Moor [9] to introduced in a three-dimensional Finsler space the intrinsic field of orthonormal frame consisting of normalized support element li, normalized torsion vector mi and the unit vector ni, orthogonal to both li and mi. Various aspects of three-dimensional Finsler spaces have been studied by Rund [5], Matsumoto [6,7,8], Rastogi [12,13,14] and others. Similarly fourdimensional Finsler spaces have been studied by Pandey and Dwivedi [10] and Rastogi [15] etc. Theory of fivedimensional Finsler spaces in terms of scalars has been studied by Pandey, Dwivedi and Gupta [11] and Dwivedi, Rastogi and Dwivedi [4]. In 1990, certain new tensors were defined and studied by Rastogi [12], while in 2019 Rastogi [14] introduced a new tensor Dijk in three-dimensional Finsler space, which is similar to tensor Cijk, but satisfies different properties like Dijk li = 0 and Dijkgjk = Di = D ni. This tensor exists only in Finsler spaces of more than two-dimensions. This tensor was further studied in four-dimensional Finsler space by Rastogi [15], but it is important to note that there are two tensors of such type in four-dimensional Finsler space. In this paper besides studying variety of tensors and their prope