On the Hypersurface of a Finsler Space with the Special Metric α+ βn+1 (α-β)n

Abstract

In the present paper, we consider a n−dimentional Finsler space Fn = (Mn,L) with (α,β)−metric L(α,β) = α + βn+1 (α−β)n which is a generalization of the metric α + β2 (α−β) considered in [9] and the hypersurface of Fn with bi(x) = ∂ib being the gradient of a scalar function b(x). We find the conditions for this hypersurface to be a hyperplane of 1st kind, 2nd kind and we also show that this hypersurface is a hyperplane of 3rd kind if and only if it is a hyperplane of f irst kind.