Extended Rectifying Curves in Minkowski 3-Space

Yılmaz, Beyhan; Gök, Ísmaíl; Yaylı, Yusuf

doi:10.1007/s00006-015-0637-7

Cited by 8 publications

(3 citation statements)

References 5 publications

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“…So, they were explored by taking advantage of the relationship between the curve on a unit dual sphere and the surface theory. Additionally, the modified Darboux vector of curve was described and it was shown that this vector is a rectifying curve [8]. Deshmukh et.al [3] developed the necessary circumstances for the centrode of a curve to be a rectifying curve in Euclidean 3-space and also, they presented the results about the dilation for rectifying curves and centrodes.…”

Section: Introductionmentioning

confidence: 99%

On rectifying curves in Minkowski 3-space

2021

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In this study, we investigate a rectifying curve by using a dilation of a unit speed curve on pseudo-sphere or pseudo-hyperbolic space and its centrode. Firstly, considering a causal character of any curve, we study the connection between Serret-Frenet apparatus of the curve on pseudo-sphere or pseudo-hyperbolic space and its dilation. Then, we extend necessary conditions when the centrode is a rectifying curve. Also, we examine some properties of centrode which is a rectifying curve.

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Section: Introductionmentioning

confidence: 99%

On rectifying curves in Minkowski 3-space

2021

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“…The space curves whose position vector always lies in its rectifying plane, called rectifying curve. To know more about the characterization of rectifying curve we refer the reader to see ( [2], [3], [4]). Recently A.…”

Section: Introductionmentioning

confidence: 99%

Darboux Rectifying curves on a smooth surface

Pal¹,

Yadav²

2021

Preprint

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“…Moreover, they showed in [11] that rectifying curves are indeed the extremal curves which satisfy the equality case of a general inequality. Since then rectifying curves have been studied by many authors, see [1,14,15,16,17,18,19,20,21] among many others. For the most recent survey on rectifying curves, see [10].…”

Section: Introductionmentioning

confidence: 99%

Differential Geometry of Rectifying Submanifolds

Chen¹

2016

International Electronic Journal of Geometry

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A space curve in a Euclidean 3-space E 3 is called a rectifying curve if its position vector field always lies in its rectifying plane. This notion of rectifying curves was introduced by the author in [6]. In this present article, we introduce and study the notion of rectifying submanifolds in Euclidean spaces. In particular, we prove that a Euclidean submanifold is rectifying if and only if the tangential component of its position vector field is a concurrent vector field. Moreover, rectifying submanifolds with arbitrary codimension are completely determined.2000 Mathematics Subject Classification. 53C40, 53C42, 53C50.

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Extended Rectifying Curves in Minkowski 3-Space

Cited by 8 publications

References 5 publications

On rectifying curves in Minkowski 3-space

On rectifying curves in Minkowski 3-space

Darboux Rectifying curves on a smooth surface

Differential Geometry of Rectifying Submanifolds

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