<abstract xmlns="http://www.w3.org/1999/xhtml">
In the geometry of curves in 𝔼3, if the principal normal vector field of a given space curve <italic>ϕ</italic> with non-zero curvatures is the principal normal vector field of another space curve <italic>ϕ</italic>*, then the curve <italic>ϕ</italic> is called a Bertrand curve and <italic>ϕ</italic>* is called Bertrand partner of <italic>ϕ</italic>. These curves have been studied in di erent space over a long period of time and found wide application in di erent areas. Therefore, we have a great knowledge of geometric properties of these curves. In this paper, revested results for spacelike Bertrand curves with non-null normal vectors will be given with the previous studies on Bertrand curves in 𝔼13. Follow this revested results, the Bertrand curve conditions of a spacelike curve are obtained in 𝔼13. In addition, new curve samples that meet the obtained conditions are constructed and the graphs of these curves are given.
</abstract>

In the geometry of curves in 𝔼3, if the principal normal vector field of a given space curve ϕ with non-zero curvatures is the principal normal vector field of another space curve ϕ*, then the curve ϕ is called a Bertrand curve and ϕ* is called Bertrand partner of ϕ. These curves have been studied in di erent space over a long period of time and found wide application in di erent areas. Therefore, we have a great knowledge of geometric properties of these curves. In this paper, revested results for spacelike Bertrand curves with non-null normal vectors will be given with the previous studies on Bertrand curves in 𝔼13. Follow this revested results, the Bertrand curve conditions of a spacelike curve are obtained in 𝔼13. In addition, new curve samples that meet the obtained conditions are constructed and the graphs of these curves are given.

Spacelike Bertrand curves in Minkowski 3-space revisited

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Spacelike Bertrand curves in Minkowski 3-space revisited"}

In the geometry of curves in 𝔼3, if the principal normal vector field of a given space curve ϕ with non-zero curvatures is the principal normal vector field...

Spacelike Bertrand curves in Minkowski 3-space revisited

Published Online: Oct 21, 2023

Page range: 87 - 109

Received: Sep 23, 2022

Accepted: Dec 22, 2022

DOI: https://doi.org/10.2478/auom-2023-0033

Keywords
Minkowski 3-space, Bertrand curves, Non-null curves

© 2023 Hatice Altın Erdem et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Spacelike Bertrand curves in Minkowski 3-space revisited

Published Online: Oct 21, 2023

Page range: 87 - 109

Received: Sep 23, 2022

Accepted: Dec 22, 2022

DOI: https://doi.org/10.2478/auom-2023-0033

KeywordsMinkowski 3-space, Bertrand curves, Non-null curves

© 2023 Hatice Altın Erdem et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Minkowski 3-space, Bertrand curves, Non-null curves