反规范定义的次洛伦兹极值

IF 0.8 4区数学 Q2 MATHEMATICS

Differential Equations Pub Date : 2024-07-08 DOI:10.1134/s001226612403008x

A. V. Podobryaev

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引用次数: 0

摘要

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。

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Sub-Lorentzian Extremals Defined by an Antinorm

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.

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来源期刊

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.