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H 1 Some projective invariants of convex domains coming from differential geometry

Auteurs : Loftin, John C. (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : I will discuss some projective differential geometric invariants of properly convex domains arising from affine dfferential geometry. Consider a properly convex domain $\Omega $ in $R^n\subset RP^n$, and the cone $C$ over $\Omega $ in $R^{n+1}$. Then Cheng-Yau have shown that there is a unique hyperbolic affine sphere which is contained in $C$ and asymptotic to the boundary $\partial C$. The hyperbolic affine sphere is invariant under special linear automorphisms of $C$ , and carries an invariant complete Riemannian metric of negative Ricci curvature, the Blaschke metric. The Blaschke metric descends to a projective-invariantmetric on $\Omega $.
    I will also address the relationship between the Blaschke metric and Hilbert metric, which is recent and is due to Benoist-Hulin. At the end, I will discuss applications to the geometry of real projective structures on surfaces.

    Codes MSC :
    53A15 - Affine differential geometry
    53C21 - Methods of Riemannian geometry, including PDE methods; curvature restrictions

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 08/10/14
      Date de captation : 16/06/14
      Collection : Research talks ; Geometry
      Format : quicktime ; audio/x-aac
      Durée : 01:14:34
      Domaine : Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2014-06-16_Loftin.mp4

    Informations sur la rencontre

    Nom de la rencontre : Geometry and dynamics of Finsler manifolds / Géométrie et dynamiques des espaces de Finsler
    Organisateurs de la rencontre : Alvarez Paiva, Juan-Carlos ; Vernicos, Constantin ; Yang, Deane
    Dates : 16/06/14 - 20/06/14
    Année de la rencontre : 2014

    Citation Data

    DOI : 10.24350/CIRM.V.18606403
    Cite this video as: Loftin, John C. (2014). Some projective invariants of convex domains coming from differential geometry. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18606403
    URI : http://dx.doi.org/10.24350/CIRM.V.18606403


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