Theory of hypersurfaces of a Finsler space with generalized square metric

The emergence of generalized square metrics in Finsler geometry can be attributed to various classification concerning (α, β})-metrics. They have excellent geometric properties in Finsler geometry. Within the scope of this research paper, we have conducted an investigation into the generalized square metric denoted as F(x,y)=(α(x,y)+β}(x,y))^(n+1)/(α^n (x,y)) focusing specifically on its application to the Finslerian hypersurface. Furthermore, the classification and existence of first, second, and third kind of hyperplanes of the Finsler manifold has been established.