Generalized pseudo null Bertrand curves in semi-Euclidean 4-space with index 2

Uçum, Ali; Keçilioğlu, Osman; İlarslan, Kazım

doi:10.1007/s12215-016-0246-x

Cited by 3 publications

(2 citation statements)

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“…3-space and Minkowski space-time (see [1,2,7,11,[24][25][26]28]) as well as in Euclidean space. In addition, in [27,30], the authors studied (1, 3)-type Bertrand curves in semi-Euclidean 4-space with index 2.…”

Section: Introductionmentioning

confidence: 99%

New approach to timelike Bertrand curves in 3-dimensional Minkowski space

Erdem,

Uçum,

İlarslan

et al. 2023

Carpathian Math. Publ.

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In the theory of curves in Euclidean $3$-space, it is well known that a curve $\beta $ is said to be a Bertrand curve if for another curve $\beta^{\star}$ there exists a one-to-one correspondence between $\beta $ and $\beta^{\star}$ such that both curves have common principal normal line. These curves have been studied in different spaces over a long period of time and found wide application in different areas. In this article, the conditions for a timelike curve to be Bertrand curve are obtained by using a new approach in contrast to the well-known classical approach for Bertrand curves in Minkowski $3$-space. Related examples that meet these conditions are given. Moreover, thanks to this new approach, timelike, spacelike and Cartan null Bertrand mates of a timelike general helix have been obtained.

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Section: Introductionmentioning

confidence: 99%

New approach to timelike Bertrand curves in 3-dimensional Minkowski space

Erdem,

Uçum,

İlarslan

et al. 2023

Carpathian Math. Publ.

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“…Bertrand curves and their characterizations were studied by many researchers in Minkowski 3-space and Minkowski space-time (see [1], [2], [6], [7], [11]) as well as in Euclidean space. In addition, in [12] and [13], the authors studied (1, 3)-type Bertrand curves in semi-Euclidean 4-space with index 2.…”

Section: Introductionmentioning

confidence: 99%

On Timelike Bertrand Curves in Minkowski 3-Space

Uçum¹,

İlarslan²

2016

Honam Mathematical Journal

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Abstract. In this paper, we study the timelike Bertrand curves in Minkowski 3-space. Since the principal normal vector of a timelike curve is spacelike, the Bertrand mate curve of this curve can be a timelike curve, a spacelike curve with spacelike principal normal or a Cartan null curve, respectively. Thus, by considering these three cases, we get the necessary and sufficient conditions for a timelike curve to be a Bertrand curve. Also we give the related examples.

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