Theory of hypersurfaces of a Finsler space with the generalized square metric

다국어 초록 (Multilingual 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 $F(x,y)=\frac{[\alpha(x,y)+\beta(x,y)]^{n+1}}{[\alpha(x,y)]^n}$, 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.