2016
DOI: 10.1142/s0219887816501127
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On Darboux rotation axis of lightlike curves

Abstract: In this paper, by used Frenet trihedron for a lightlike curve, the motion of Darboux rotation axis is seperated to two simultaneous rotation motions. These rotation motions are that tangent and normal vectors of lightlike curve rotate around each other. But, the angular speeds of them are different. Then, by doing the similar operations, we obtain that Darboux axis rotates around spacelike vector of Frenet trihedron of the lightlike curve and this spacelike vector rotates around Darboux axis. Consequently, we … Show more

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Cited by 6 publications
(2 citation statements)
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“…Among the non-Euclidean geometries, Lorentzian geometry has the most well known applications [3,7,15,17,18,6]. Then, Lorentzian geometry is a very common research area of di¤erential geometry with physical problems on integrable systems, soliton theory, ‡uid dynamics, …eld theories, etc.…”
Section: Introductionmentioning
confidence: 99%
“…Among the non-Euclidean geometries, Lorentzian geometry has the most well known applications [3,7,15,17,18,6]. Then, Lorentzian geometry is a very common research area of di¤erential geometry with physical problems on integrable systems, soliton theory, ‡uid dynamics, …eld theories, etc.…”
Section: Introductionmentioning
confidence: 99%
“…) are indicated in [1,2], respectively. Among the non-Euclidean geometries, Lorentzian geometry has the most well known applications [7,8,9,10]. Lorentzian geometry is a branch of study that deals with soliton theory, fluid dynamics, integrable systems, field theories and other physical concerns [11,12,13,14].…”
Section: Introductionmentioning
confidence: 99%