Sub-Lorentzian Extremals Defined by an Antinorm
Pub Date : 2024-07-08
DOI:10.1134/s001226612403008x
引用次数: 0
Abstract
We consider a left-invariant sub-Lorentzian structure on a Lie group. This structure is assumed to be defined by a closed convex salient cone in the corresponding Lie algebra and a continuous antinorm associated with this cone. We derive the Hamiltonian system for sub-Lorentzian extremals and give conditions under which normal extremal trajectories keep their causal type. Tangent vectors of abnormal extremal trajectories are either lightlike or are tangent vectors of sub-Riemannian abnormal extremal trajectories for the sub-Riemannian distribution spanned by the cone.
反规范定义的次洛伦兹极值
摘要 我们考虑了在一个李群上的左不变亚洛伦兹结构。该结构被假定为由相应的李代数中的闭凸突出锥和与该锥相关的连续反规范所定义。我们推导了次洛伦兹极值的哈密顿系统，并给出了正常极值轨迹保持其因果类型的条件。异常极值轨迹的切向量要么是轻型的，要么是锥体所扫描的亚黎曼分布的亚黎曼异常极值轨迹的切向量。
本文章由计算机程序翻译，如有差异，请以英文原文为准。
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