On normal curves and their characterizations in Lorentzian n-space

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...

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Bibliographic Details
Published inAIMS mathematics Vol. 5; no. 4; pp. 3510 - 3524
Main Author Boyacıoğlu Kalkan, Özgür
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2020
Subjects
curvatures
frenet equations
lorentzian n -space
non-null normal curves
null normal curves
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2020228