Theory of hypersurfaces of a Finsler space with generalized square metric

Abstract

The emergence of generalized square metrics in Finsler geometry can be attributed to various classification concerning ({\alpha}, \beta})-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)=({\alpha}(x,y)+\beta}(x,y))^(n+1)/({\alpha}^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.