A Frobenius theorem for Cartan geometries, with applications

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dc.creatorMelnick, Karin
dc.date2008-12-03
dc.date2008-12-31
dc.date.accessioned2026-07-07T12:22:45Z
dc.date.available2026-07-07T12:22:45Z
dc.descriptionWe prove analogues for Cartan geometries of Gromov's major theorems on automorphisms of rigid geometric structures. The starting point is a Frobenius theorem, which says that infinitesimal automorphisms of sufficiently high order integrate to local automorphisms. Consequences include a stratification theorem describing the configuration of orbits for local Killing fields in a compact real-analytic Cartan geometry, and an open-dense theorem in the smooth case, which says that if there is a dense orbit, then there is an open, dense, locally homogeneus subset. Combining the Frobenius theorem with the embedding theorem of Bader, Frances, and the author gives a representation theorem that relates the fundamental group of the manifold with the automorphism group.
dc.description32 pages. Several minor corrections in new version
dc.identifierhttps://arxiv.org/abs/0812.0624
dc.identifierhttp://arxiv.org/abs/0812.0624
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/213758
dc.subjectDifferential Geometry
dc.subject53A35
dc.titleA Frobenius theorem for Cartan geometries, with applications
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