Year: 2025
Type: article
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.
Source: TURKISH JOURNAL OF MATHEMATICS
Authors: HÉCTOR GUERRERO MORA, WILLY SIERRA
Institution: University of Cauca
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Funder: Universidad del Cauca
OpenAlex ID: W4410430515