On normal curves and their characterizations in Lorentzian n-space

Özgür Boyacıoğlu Kalkan; Özgür Boyacıoğlu Kalkan

doi:10.3934/math.2020228

AIMS Mathematics

2020, Volume 5, Issue 4: 3510-3524. doi: 10.3934/math.2020228

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Research article

On normal curves and their characterizations in Lorentzian n-space

Özgür Boyacıoğlu Kalkan ^,

Afyon Vocational School, Afyon Kocatepe University, 03200, Afyonkarahisar-Turkey

Received: 12 December 2019 Accepted: 30 March 2020 Published: 09 April 2020
MSC : 53A04, 53A35, 53B30

This paper deals with the generalization of null and non-null normal curves in Lorentzian n -space E₁ⁿ. We reveal necessary and sufficient condition for a curve to be a normal curve in Lorentzian n -space E₁ⁿ. We obtain the relationship between the curvatures for any arclength parametrized curve to be congruent to a normal curve in E₁ⁿ. Moreover, we give differential equations by introducing a differentiable function f(s) which can be solved explicitly for a curve to be congruent to a normal curve.
- Lorentzian n -space,
- null normal curves,
- non-null normal curves,
- Frenet equations,
- curvatures
Citation: Özgür Boyacıoğlu Kalkan. On normal curves and their characterizations in Lorentzian n-space[J]. AIMS Mathematics, 2020, 5(4): 3510-3524. doi: 10.3934/math.2020228

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Abstract

This paper deals with the generalization of null and non-null normal curves in Lorentzian n -space E₁ⁿ. We reveal necessary and sufficient condition for a curve to be a normal curve in Lorentzian n -space E₁ⁿ. We obtain the relationship between the curvatures for any arclength parametrized curve to be congruent to a normal curve in E₁ⁿ. Moreover, we give differential equations by introducing a differentiable function f(s) which can be solved explicitly for a curve to be congruent to a normal curve.

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