Timelike acc-slant curves in Minkowski 3-space

Hasan Altınbaş; Hasan Altınbaş

doi:10.3934/math.2025658

AIMS Mathematics

2025, Volume 10, Issue 6: 14617-14628. doi: 10.3934/math.2025658

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Research article

Timelike acc-slant curves in Minkowski 3-space

Hasan Altınbaş ^,

Department of Mathematics, Kırşehir Ahi Evran University, Kırşehir 40100, Turkey

Received: 24 March 2025 Revised: 12 June 2025 Accepted: 16 June 2025 Published: 26 June 2025
MSC : 53A04, 53A35

In this work, we introduced the concept of a timelike acceleration-slant curve in three-dimensional Minkowski space, characterized by the property that the scalar product of a fixed unit direction and its acceleration vector remained constant. Moreover, we provided a classification of timelike acceleration-slant curves with a non-null axis based on their curvature properties. Later on, we explored the relationships between timelike acceleration-slant curves and various notable curves, including timelike helices, timelike slant helices, timelike Lorentzian spherical curve, and timelike Salkowski curves. To further illustrate and validate the theoretical results, we utilized Mathematica to generate visual representations.
- acceleration,
- helix,
- slant helix,
- Salkowski curve,
- Minkowski 3-space
Citation: Hasan Altınbaş. Timelike acc-slant curves in Minkowski 3-space[J]. AIMS Mathematics, 2025, 10(6): 14617-14628. doi: 10.3934/math.2025658

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Abstract

In this work, we introduced the concept of a timelike acceleration-slant curve in three-dimensional Minkowski space, characterized by the property that the scalar product of a fixed unit direction and its acceleration vector remained constant. Moreover, we provided a classification of timelike acceleration-slant curves with a non-null axis based on their curvature properties. Later on, we explored the relationships between timelike acceleration-slant curves and various notable curves, including timelike helices, timelike slant helices, timelike Lorentzian spherical curve, and timelike Salkowski curves. To further illustrate and validate the theoretical results, we utilized Mathematica to generate visual representations.

References

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