On Finsler Spaces Satisfying the Condition Lm+1C = γm

Abstract

In the year 1979, M. Matsumoto has discussed non-Riemannian Finsler spaces with vanishing T-Tensor. In the paper, M. Matsumoto has shown that if a Finsler space Mn satisfy T−condition i.e. Thijk = 0, Then for such a Finsler space the function L 2C 2 of Mn is a function of position only (i.e. L2C 2 = f(x)), where L is fundamental function and C 2 is the square of length of torsion tensor Ci. In continuity of the above paper F. Ikeda in the year 1984, studied Finsler spaces L 2C 2 as a function of x in detail. In the year 1991, Ikeda considered Finsler spaces satisfying the condition L 2C 2 as to non-zero constant, which is a stronger condition. One of the author T. N. Pandey in the year 2012 studied Finsler spaces taken L 2C 2 equal to some known function of x and y i.e. L 2C 2 = f(x) + f(y). In the present paper we shall consider the combination of L and C differently and taking L m+1C = λ m, where γ is mth root metric