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)
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.
|Uncontrolled Keywords:||Pedal foliations, Gauss map, Lagrangian singularity, Legendrian singularity|
|Subjects:||57-xx MANIFOLDS AND CELL COMPLEXES|