TB_1 Lorentz Hybrid Partner Ruled Surfaces in R^3

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Hagia Sophia Journal of Geometry
Cilt: 7 Sayı: 2
TB_1 Lorentz Hybrid Partner Ruled Surfaces in R^3_1

TB_1 Lorentz Hybrid Partner Ruled Surfaces in R^3_1

Authors : Müge Cengiz, Nevin Ertuğ Gürbüz

Pages : 1-15

View : 152 | Download : 128

Publication Date : 2025-12-29

Article Type : Research Paper

Abstract :In this paper, we derive the first and second fundamental forms, as well as the Gaussian and mean curvatures, of $TB_{1}$ Lorentz hybrid partner ruled surfaces in three distinct cases. We establish the necessary and sufficient conditions for these surfaces to be developable and minimal with respect to the Lorentz hybrid frame in Minkowski 3-space. Moreover, we demonstrate that the $\\\\sigma $-parameter curves are asymptotic but not geodesic, while the $v$-parameter curves are simultaneously geodesic and asymptotic. We investigate the necessary and sufficient conditions for the $\\\\sigma $- and $v$-parameter curves of $TB_{1}$ Lorentz hybrid partner ruled surfaces to be simultaneously lines of curvature for three cases.
Keywords : Ortak regle yüzeyler, minimal yüzey, Minkowski 3-uzay, Hibrit çatı

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