Show simple item record

dc.contributor.authorKruglikov, Boris
dc.contributor.authorMatveev, Vladimir S.
dc.date.accessioned2023-01-10T14:34:51Z
dc.date.available2023-01-10T14:34:51Z
dc.date.issued2022-10-15
dc.description.abstractGiven a smooth family of unparameterized curves such that through every point in every direction there passes exactly one curve, does there exist a Lagrangian with extremals being precisely this family? It is known that in dimension 2 the answer is positive. In dimension 3, it follows from the work of Douglas that the answer is, in general, negative. We generalise this result to all higher dimensions and show that the answer is actually negative for almost every such a family of curves, also known as path structure or path geometry. On the other hand, we consider path geometries possessing infinitesimal symmetries and show that path and projective structures with submaximal symmetry dimensions are variational. Note that the projective structure with the submaximal symmetry algebra, the so-called Egorov structure, is not pseudo-Riemannian metrizable; we show that it is metrizable in the class of Kropina pseudo-metrics and explicitly construct the corresponding Kropina Lagrangian.en_US
dc.identifier.citationKruglikov, Matveev. Almost every path structure is not variational. General Relativity and Gravitation. 2022;54(10)en_US
dc.identifier.cristinIDFRIDAID 2080935
dc.identifier.doi10.1007/s10714-022-03006-2
dc.identifier.issn0001-7701
dc.identifier.issn1572-9532
dc.identifier.urihttps://hdl.handle.net/10037/28134
dc.language.isoengen_US
dc.publisherSpringeren_US
dc.relation.journalGeneral Relativity and Gravitation
dc.rights.accessRightsopenAccessen_US
dc.rights.holderCopyright 2022 The Author(s)en_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0en_US
dc.rightsAttribution 4.0 International (CC BY 4.0)en_US
dc.titleAlmost every path structure is not variationalen_US
dc.type.versionpublishedVersionen_US
dc.typeJournal articleen_US
dc.typeTidsskriftartikkelen_US
dc.typePeer revieweden_US


File(s) in this item

Thumbnail

This item appears in the following collection(s)

Show simple item record

Attribution 4.0 International (CC BY 4.0)
Except where otherwise noted, this item's license is described as Attribution 4.0 International (CC BY 4.0)