Turkish Journal of Mathematics
Abstract
In this article, using the concept of a Killing vector field along a curve, we extend certain results concerning a family of curves—previously studied in three-dimensional Euclidean space—to the setting of three-dimensional Minkowski space. Depending on the causal character of the curve, we derive Lancret-type results that establish the necessary and sufficient conditions for the existence of this family in three-dimensional Minkowski space. We determine the intrinsic equation of this family in three cases: (i) when the curve is nonnull with a nonnull acceleration vector, (ii) when the curve is spacelike with a null acceleration vector, and (iii) when the curve is null. In this article, using the concept of a Killing vector field along a curve, we extend certain results concerning a family of curves—previously studied in three-dimensional Euclidean space—to the setting of three-dimensional Minkowski space. Depending on the causal character of the curve, we derive Lancret-type results that establish the necessary and sufficient conditions for the existence of this family in three-dimensional Minkowski space. We determine the intrinsic equation of this family in three cases: (i) when the curve is nonnull with a nonnull acceleration vector, (ii) when the In this article, using the concept of a Killing vector field along a curve, we extend certain results concerning a family of curves—previously studied in three-dimensional Euclidean space—to the setting of three-dimensional Minkowski space. Depending on the causal character of the curve, we derive Lancret-type results that establish the necessary and sufficient conditions for the existence of this family in three-dimensional Minkowski space. We determine the intrinsic equation of this family in three cases: (i) when the curve is nonnull with a nonnull acceleration vector, (ii) when the curve is spacelike with a null acceleration vector, and (iii) when the curve is null.
DOI
10.55730/1300-0098.3587
Keywords
Curves, intrinsic equation, Killing vector fields, Lancret-type results, Minkowski space
First Page
244
Last Page
260
Publisher
The Scientific and Technological Research Council of Türkiye (TÜBİTAK)
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
GUERRERO MORA, H, & SIERRA, W (2025). Lancret-type results for a new family of curves in Minkowski 3-space. Turkish Journal of Mathematics 49 (3): 244-260. https://doi.org/10.55730/1300-0098.3587
