Pedal foliations and Gauss maps of hypersurfaces in Euclidean space
Journal of Singularities, Tome 6 (2012), pp. 84-97
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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.
@article{10_5427_jsing_2012_6g,
author = {Shyuichi Izumiya and Masatomo Takahashi},
title = {Pedal foliations and {Gauss} maps of hypersurfaces in {Euclidean} space},
journal = {Journal of Singularities},
pages = {84--97},
publisher = {mathdoc},
volume = {6},
year = {2012},
doi = {10.5427/jsing.2012.6g},
url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2012.6g/}
}
TY - JOUR AU - Shyuichi Izumiya AU - Masatomo Takahashi TI - Pedal foliations and Gauss maps of hypersurfaces in Euclidean space JO - Journal of Singularities PY - 2012 SP - 84 EP - 97 VL - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.5427/jsing.2012.6g/ DO - 10.5427/jsing.2012.6g ID - 10_5427_jsing_2012_6g ER -
%0 Journal Article %A Shyuichi Izumiya %A Masatomo Takahashi %T Pedal foliations and Gauss maps of hypersurfaces in Euclidean space %J Journal of Singularities %D 2012 %P 84-97 %V 6 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.5427/jsing.2012.6g/ %R 10.5427/jsing.2012.6g %F 10_5427_jsing_2012_6g
Shyuichi Izumiya; Masatomo Takahashi. Pedal foliations and Gauss maps of hypersurfaces in Euclidean space. Journal of Singularities, Tome 6 (2012), pp. 84-97. doi: 10.5427/jsing.2012.6g
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