Lancret-type results for a new family of curves in Minkowski 3-space

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.