Rad HAZU, Matematičke znanosti, Vol. 30 (2026), 159-167. \( \)

ELLIPTIC CURVES ASSOCIATED TO A SPACELIKE CURVE IN THE LORENTZ PLANE

Mircea Crasmareanu

Faculty of Mathematics, University “Al. I. Cuza”, 700506 Iaşi, Romania
e-mail:mcrasm@uaic.ro

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.

2020 Mathematics Subject Classification.   53A04, 53A45, 53A55

Key words and phrases.   Lorentz plane, spacelike curve, curvature, elliptic curve

Full text (PDF) (free access)

https://doi.org/10.21857/mjrl3urdk9

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