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Automorphisms of rigid geometric structures à la Zimmer–Gromov

By Karin Melnick

Appears in collection : Group Actions and Rigidity: Around the Zimmer Program / Actions de Groupes et Rigidité : Autour du programme de Zimmer

This talk begins with examples of rigid and non-rigid geometric structures, followed by an in-depth discussion of the Fundamental Theorem of Riemannian Geometry, on existence and uniqueness of a torsion-free connection compatible with a Riemannian metric. This result is interpreted as giving a framing on the orthonormal frame bundle uniquely determined by the metric. It is seen to be a consequence of the vanishing of the first prolongation of the orthogonal Lie algebra.

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Citation data

  • DOI 10.24350/CIRM.V.20159403
  • Cite this video Melnick, Karin (16/04/2024). Automorphisms of rigid geometric structures à la Zimmer–Gromov. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20159403
  • URL https://dx.doi.org/10.24350/CIRM.V.20159403

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