L^3 de Spacelike Odak Eğrisinin Harmonik Eğrilikleri Üzerine Bir Çalışma

Öz

Bu makalede, [6]’da verilen, indeksi 1 olan Lorentz 3-uzay L^3’deki spacelike odak eğrisinin Frenet denklemlerini inceliyoruz. Eğrinin sırasıyla teğet, esas normal ve binormal Frenet vektörleri olan T, N ve W’yi ve Frenet denklemlerini kullanarak, spacelike odak eğrisi için bazı önemli tanımlar, teoremler ve sonuçlar veriyoruz. Ek olarak, indeksi 1 olan üç boyutlu Lorentz uzayındaki spacelike odak eğrisini, harmonik eğrilikler açısından inceledik. Son olarak, bir örnekle L^3’ deki spacelike odak eğrisini ve Lorentz dairesel helisini elde ettik.

Anahtar Kelimeler

• lorentz uzayı
• harmonik eğriler
• odak eğrisi

A Study on Harmonic Curvatures of a Spacelike Focal Curve in L^3

Öz

In this paper,we study with Frenet equations which are given in [6] of a spacelike focal curve in Lorentz 3-space L^3 with index 1. By using the T, N and W are the tangent, the principal normal and the binormal Frenet vectors of the curve respectively and Frenet equations, we give some important definitions, theorems and results for spacelike focal curve. Addtionally, we examined a spacelike focal curve in the three-dimensional Lorentz space with index 1 in terms of harmonic curvatures. Finally, with a example obtained a spacelike focal curve and the Lorentzian circular helix, of a spacelike curve in L^3.

Anahtar Kelimeler

• lorentzian space
• harmonic curvates
• focal curve

Kaynakça

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