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Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti, No. 570=30, 2026.

Original scientific paper

https://doi.org/10.21857/mjrl3urdk9

Elliptic curves associated to a spacelike curve in the Lorentz plane

Mircea Crasmareanu orcid id orcid.org/0000-0002-5230-2751 ; Faculty of Mathematics, University “Al. I. Cuza”, 700506 Iaşi, Romania

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page 159-167

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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.

Keywords

Lorentz plane; spacelike curve; curvature; elliptic curve

Hrčak ID:

344368

URI

https://hrcak.srce.hr/344368

Publication date:

10.2.2026.

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