{"title":"Sub-Lorentzian Extremals Defined by an Antinorm","authors":"A. V. Podobryaev","doi":"10.1134/s001226612403008x","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider a left-invariant sub-Lorentzian structure on a Lie group. This structure is\nassumed to be defined by a closed convex salient cone in the corresponding Lie algebra and a\ncontinuous antinorm associated with this cone. We derive the Hamiltonian system for\nsub-Lorentzian extremals and give conditions under which normal extremal trajectories keep their\ncausal type. Tangent vectors of abnormal extremal trajectories are either lightlike or are tangent\nvectors of sub-Riemannian abnormal extremal trajectories for the sub-Riemannian distribution\nspanned by the cone.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s001226612403008x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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.
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