Pedal foliations and Gauss maps of hypersurfaces in Euclidean space

Shyuichi Izumiya and Masatomo Takahashi

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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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.


Pedal foliations, Gauss map, Lagrangian singularity, Legendrian singularity

Mathematical Subject Classification:

57R45, 58Kxx

Author(s) information:

Shyuichi Izumiya Masatomo Takahashi
Department of Mathematics Muroran Institute of Technology
Hokkaido University Muroran 050-8585, Japan
Sapporo 060-0810, Japan
email: email: