Pedal foliations and Gauss maps of hypersurfaces in Euclidean space

Journal of Singularities
volume 6 (2012), 84-97
Proceedings of the Workshop on Singularities in Geometry and Applications, Będlewo, 5 – 21 May 2011

Received: 14 December 2011. Received in revised form: 1 March 2012.

DOI: 10.5427/jsing.2012.6g

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Abstract:

The singular point of the Gauss map of a hypersurface in Euclidean space is the parabolic point where the Gauss-Kronecker curvature vanishes. It is well-known that the contact of a hypersurface with the tangent hyperplane at a parabolic point is degenerate. The parabolic point has been investigated in the previous research by applying the theory of Lagrangian or Legendrian singularities. In this paper we give a new interpretation of the singularity of the Gauss map from the view point of the theory of wave front propagations.

Keywords:

Pedal foliations, Gauss map, Lagrangian singularity, Legendrian singularity

Mathematical Subject Classification:

57R45, 58Kxx

Author(s) information: