# Pedal foliations and Gauss maps of hypersurfaces in Euclidean space

Preprint Series # 1001
Izumiya, Shyuichi and Takahashi, Masatomo Pedal foliations and Gauss maps of hypersurfaces in Euclidean space. (10 March 2012); (Submitted)

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## Abstract

he 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.

Item Type: Preprint Pedal foliations, Gauss map, Lagrangian singularity, Legendrian singularity 57-xx MANIFOLDS AND CELL COMPLEXES 2185