4-Boyutlu Lorentz Minkowski Uzayında Null Olmayan Ortak İzoasimptotik Eğrili Hiperyüzey Aileleri

Year 2022, Issue: 38, 99 - 109, 31.08.2022

Çiğdem Turan , Mustafa Altın , Hacı Bayram Karadağ

https://doi.org/10.31590/ejosat.1093177

Abstract

Bu çalışmada, E_^4 Lorentz Minkowski uzayında null olmayan Frenet vektörlere sahip spacelike ve timelike eğrilerinden geçen hiperyüzeylerin parametrik denklemi, bu eğrinin Frenet çatısı yardımıyla ifade edildi. Ayrıca E_^4 de spacelike ve timelike eğrilerinin hiperyüzey üzerinde ortak izoasimptotik olması için gerekli ve yeterli koşullar verilerek hiperyüzey aileleri oluşturuldu. Daha sonra sapma fonksiyonları yardımıyla elde edilen bu koşullar sadeleştirildi. Son olarak, örneklerle çalışma desteklendi ve belli izdüşüm metodları kullanılarak örneklerin grafikleri çizildi.

Keywords

4-Boyutlu Lorentz Minkowski Uzayı, Spacelike ve Timelike İzoasimptotik Eğri, Hiperyüzey Aileleri

Hypersurfaces Families with Common Non-Null Isoasymptotic Curve in Lorentz Minkowski 4-Space

Abstract

In this study, the parametric equation of hypersurfaces passing through the spacelike and timelike curves that has non-null Frenet vectors in E_1^4 Lorentz Minkowski space was expressed with the help of this curve is Frenet frame. Furthermore, hypersurface families were created by giving necessary and sufficient conditions so that the spacelike and timelike curves on E_1^4 is common isoasymptotic on the hypersurface. Then, these conditions obtained with the help of deviation marching-scale functions were simplified. Finally, the study was supported with examples and the graphics were drawn using certain projection methods.

Keywords

Lorentz Minkowski 4-Space, Spacelike and Timelike Isoasymptotic Curve, Hypersurface Families

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