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

2025/08/24 by Aydin, Muhittin Evren, López, Rafael
#49K05 #53A10 #74G65 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.17317

Abstract

In this paper, we study hypersurfaces in Lorentz-Minkowski space \mathbbLⁿ⁺¹ that are stationary for the moment of inertia with respect to the origin. After giving examples and applications of the maximum principle, we classify, in \mathbbL³, all stationary surfaces that are ruled surfaces. We prove that planes are the only cylindrical stationary surfaces. If the surface is not cylindrical, the classification depends on the causal character of the rulings. In addition, we provide explicit parametrizations of all ruled stationary surfaces.

Citations

• Extension of a problem of Euler in Lorentz-Minkowski plane
• Stationary surfaces for the moment of inertia with constant Gauss curvature
• Axisymmetric stationary surfaces for the moment of inertia
• Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici lattissimo sensu accepti

Related

• Axisymmetric stationary surfaces for the moment of inertia
• Stationary bands in three-dimensional Minkowski space
• Two classification results for stationary surfaces of the least moment of inertia
• Spacelike surfaces in Minkowski space satisfying a linear relation between their principal curvatures
• Singular Miminal Ruled Surfaces