Elliptic curves associated to a spacelike curve in the Lorentz plane
Abstract
We associate an elliptic curve to each point of a natural parametrization of a spacelike naturally parametrized curve \(C\) in the Lorentz plane. The main tool of our study is the curvature of \(C\) and the equilateral hyperbola appears as a remarkable example since its elliptic curve is a CM one. Other two elliptic curves are obtained with this approach, the second one corresponding to the adjoint differential equation of the first, which in turn, is associated to a Lorentzian version of the logarithmic spiral.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Advanced Differential Geometry Research
Algebraic and Geometric Analysis
Publication details
- Journal / source
- Rad Hrvatske akademije znanosti i umjetnosti Matematičke znanosti
- Publisher
- Croatian Academy of Sciences and Arts
- Volume
- 30
- Pages
- 159–167
- Publication date
- 1 January 2026
- Language
- EN