• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.781-788
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• 2018

In the present paper, we have studied the Finslerian hypersurfaces and generalized ${\beta}$-conformal change of Finsler metric. The relations between the Finslerian hypersurface and the other which is Finslerian hypersurface given by generalized ${\beta}$-conformal change have been obtained. We have also proved that generalized ${\beta}$-conformal change makes three types of hypersurfaces invariant under certain conditions.

• Journal of applied mathematics & informatics
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• v.42 no.4
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• pp.879-897
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• 2024

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