Hypersurfaces of a Finsler Manifold with the Square Root Metric

The study of Finsler manifold with (α,β)-metric is very imporatant aspect of Finsler geometry in terms of its applications. Finsler metrics are extensively used in special theory of relativelty, information science, thermodynamics and geometric optics of anisotropic media. The study of hypersurfaces of a Finsler manifold with some important and special (α,β)-metric has already been studied. The emergence of square root metrics in Finsler geometry can be attributed to various classification concerning (α,β) metric. They have also excellent geometric properties in Finsler geometry. In this paper, we have charecterized the hypersurfaces of a Finsler space with square root (α,β)-metric denoted by F=√(α(α+β)), where α=√(a_ij (x)y^i y^j ) is a Riemannian manifold and β=b_i (x)y^i is a differential 1-form on the Finsler manifold (M,F). Furthermore, it has been found the criterion of hypersurface to be a hyperplane of first kind, hyperplane of second kind and not the hyperplane of the third kind.