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H 1 Singularities of tangent surfaces and generalised frontals

Auteurs : Ishikawa, Goo (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Given a space curve, the surface ruled by tangent lines to the curve is called the tangent surface or the tangent developable to the curve. Tangent surfaces were studied by many mathemati- cians, Euler, Monge, Cayley, etc. The tangent surface has necessarily singularities along the original curve (curve of regression). The singularities are classified by Cleave, Mond, Arnold, Shcherbak and so on. In this talk we provide several generalisations of the known classification results. In particular we consider, in one direction, tangent surfaces to possibly singular curves in an ambient space of any dimension with any affine connection. In another direction, we study "abnormal" tangent surfaces to integral curves of a Cartan distribution in five space. The exposition will be performed via a generalised notion of "frontal".

    Codes MSC :
    53A20 - Projective differential geometry
    57R45 - Singularities of differentiable mappings
    58K40 - Classification; finite determinacy of map germs

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 03/03/15
      Date de captation : 17/02/15
      Collection : Research talks ; Algebraic and Complex Geometry
      Format : quicktime ; audio/x-aac
      Durée : 00:48:42
      Domaine : Algebraic & Complex Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-02-17_Ishikawa.mp4

    Informations sur la rencontre

    Nom de la rencontre : Real singularities and applications / Singularités réelles et applications
    Organisateurs de la rencontre : Dutertre, Nicolas ; Trotman, David
    Dates : 16/02/15 - 20/02/15
    Année de la rencontre : 2015
    URL Congrès : http://chairejeanmorlet-1stsemester2015....

    Citation Data

    DOI : 10.24350/CIRM.V.18703803
    Cite this video as: Ishikawa, Goo (2015). Singularities of tangent surfaces and generalised frontals. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18703803
    URI : http://dx.doi.org/10.24350/CIRM.V.18703803


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