The Hypersurface of a Finsler Space with Special $(\alpha,\beta)$-metric $ F = \alpha + \frac{\beta^{n+1}}{\alpha^n}$

Abstract

A hypersurface of a Finsler space with a special $(\alpha, \beta)$ -metric involves studying intrinsic geometric properties like curvature and hyperplanes. The concept of $(\alpha,\beta)$-metric was introduced by M. Matsumoto in 1972 [1]. In this paper, we determining when a hypersurface is a hyperplane of a specific kind and the criterion for a hypersurface of a special metric to be a hyperplane of the first kind, second kind and third kind.