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RAS MathematicsДифференциальные уравнения Differential Equations

  • ISSN (Print) 0374-0641
  • ISSN (Online) 3034-5030

SUB-LORETZIAN EXTREMALS DEFINED BY AN ANTINORM

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PII
10.31857/S0374064124030089-1
DOI
10.31857/S0374064124030089
Publication type
Article
Status
Published
Authors
A. V Podobryaev
  • Affiliation: A.K. Ailamazyan Program Systems Institute of RAS
Volume/ Edition
Volume 60 / Issue number 3
Pages
386-398
Abstract
We consider a left-invariant sub-Lorentzian structure on a Lie group. We assume that this structure is 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 that normal extremal trajectories keep their causal type. Tangent vectors of abnormal extremal trajectories are either light-like or tangent vectors of sub-Riemannian extremal trajectories for the sub-Riemannian distribution spanned by the cone.
Keywords
лоренцево многообразие сублоренцево многообразие антинорма экстремаль экстремальная траектория каузальный тип
Date of publication
18.09.2025
Year of publication
2025
Number of purchasers
0
Views
2

References

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