TB_1 Lorentz Hybrid Partner Ruled Surfaces in R^3_1

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

• Partner ruled surfaces
• Minimal surface
• Minkowski 3 space
• Hybrid frame

R^3_1' de TB_1 Lorentz Hibrit Regle Yüzeyler

Abstract

Bu makalede, üç farklı durumda TB 1 Lorentz hibrit ortak regle yüzeylerinin birinci ve ikinci temel formlarını, ayrıca Gauss ve ortalama eğriliklerini çıkarıyoruz. Bu yüzeylerin Minkowski 3-uzayında Lorentz hibrit çatısına göre açılabilir ve minimal olmaları için gerekli ve yeterli koşulları belirliyoruz. Dahası, σ-parametre eğrilerinin asimptotik ancak jeodezik olmadığını, v-parametre eğrilerinin ise aynı anda jeodezik ve asimptotik olduğunu gösteriyoruz. Üç durum için TB 1 Lorentz hibrit ortak regle yüzeylerinin σ- ve v-parametre eğrilerinin aynı anda eğrilik çizgileri olmaları için gerekli ve yeter koşulları inceliyoruz.

Keywords

• Ortak regle yüzeyler
• minimal yüzey
• Minkowski 3-uzay
• Hibrit çatı

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