Extension of a problem of Euler in Lorentz-Minkowski plane

2025/08/24 by Aydin, Muhittin Evren, López, Rafael · 1 citation
#35A15 #49Q05 #53A10 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.17314

Abstract

In this paper we study curves in Lorentz-Minkowski space \mathbbL² that are critical points of the moment of inertia with respect to the origin. This extends a problem posed by Euler in the Lorentzian setting. We obtain explicit solutions for stationary curves in \mathbbL² distinguishing if the curve is spacelike or timelike. We also give a method to carry stationary spacelike curves into stationary timelike curves and vice versa via symmetries and inversions about the lightlike cone. Finally, we solve the problem of maximizing the energy among all spacelike curves joining two given points which are collinear with the origin.

Citations

• Axisymmetric stationary surfaces for the moment of inertia
• Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici lattissimo sensu accepti

Cited by

• Classification of ruled surfaces in Lorentz-Minkowski space that are stationary for the moment of inertia

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