On harmonic curvatures of a Frenet curve in Lorentzian space

Külahçı, Fatih; Bektaş, Mehmet; Ergüt, Mahmut

doi:10.1016/j.chaos.2008.07.013

Cited by 14 publications

(10 citation statements)

References 9 publications

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“…Harmonic curvature functions were defined earlier byÖzdamar and Hacısalihoglu [20]. Recently, many studies have been reported on generalized helices and slant helices using the harmonic curvatures in Euclidean spaces and Minkowski spaces [6,11,17]. Then, Okuyucu et al [19] defined slant helices in three dimensional Lie groups with a bi-invariant metric and obtained some characterizations using their harmonic curvature function.…”

Section: Introductionmentioning

confidence: 99%

Bertrand curves in three dimensional Lie groups

Okuyucu¹,

Gk²,

Yaylı³

et al. 2017

MMN

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In this paper, we give the definition of harmonic curvature function some special curves such as helix, slant curves, Mannheim curves and Bertrand curves. Then, we recall the characterizations of helices [8], slant curves (see [19]) and Mannheim curves (see [12]) in three dimensional Lie groups using their harmonic curvature function.Moreover, we define Bertrand curves in a three dimensional Lie group G with a bi-invariant metric and the main result in this paper is given as (Theorem 3.4): A curve α : I ⊂ R →G with the Frenet apparatus {T, N, B, κ, τ } is a Bertrand curve if and only if λκ + µκH = 1 where λ, µ are constants and H is the harmonic curvature function of the curve α.

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Section: Introductionmentioning

confidence: 99%

Bertrand curves in three dimensional Lie groups

Okuyucu¹,

Gk²,

Yaylı³

et al. 2017

MMN

View full text Add to dashboard Cite

show abstract

“…Harmonic curvature functions have been defined byÖzdamar and Hacısalihoglu [16]. Recently, many studies have been reported on generalized helices and slant helices using the harmonic curvatures in Euclidean spaces and Minkowski spaces [2,6,11]. Then, Okuyucu et al [14] have defined slant helices in three dimensional Lie groups with a bi-invariant metric and obtained some characterizations using their harmonic curvature functions.…”

Section: Introductionmentioning

confidence: 99%

On Mannheim partner curves in three dimensional Lie groups

Gök¹,

Okuyucu²,

Ekmekçi³

et al. 2014

MMN

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“…In particular, many works with AW(k)-type curves have been done by several authors. For example, in [9], the authors gave curvature conditions and charaterizations related to these curves in R n . Also, in [10], they investigated curves of AW(k)-type in the three-dimensional null cone and gave curvature conditions of these kind of curves.…”

Section: Introductionmentioning

confidence: 99%

Classiffications of special curves in the three-dimensional Lie group

Lee¹,

Lee²

2016

ijma

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In the present paper, we define a Bertrand curve in the three-dimensional Lie group G with a bi-invariant metric, and we show a Frenet curve α with Frenet curvatures k 1 and k 2 in G is a Bertrand curve if and only if it satisfies Ak 1 + B(k 2 +k 2) = 1, where A and B are some constants andk 2 = 1/2 [V 1 , V 2 ], V 3. Also, we investigate a Bertrand curve using the Frenet curvature conditions of AW(k)-type (k = 1, 2, 3) curves in G.

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On harmonic curvatures of a Frenet curve in Lorentzian space

Cited by 14 publications

References 9 publications

Bertrand curves in three dimensional Lie groups

Bertrand curves in three dimensional Lie groups

On Mannheim partner curves in three dimensional Lie groups

Classiffications of special curves in the three-dimensional Lie group

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