Goo Ishikawa: Singularities of tangent surfaces and generalised frontal

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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".

Recording during the thematic meeting: «Real singularities and applications» the February 17, 2015 at the Centre International de Rencontres Mathématiques (Marseille, France)

Film maker: Guillaume Hennenfent