Singularities of one-parameter pedal unfoldings of spherical pedal curves

Journal of Singularities
volume 2 (2010), 160-169
Proceedings of Singularities in Aarhus, August 2009

Received: 1 December 2009

DOI: 10.5427/jsing.2010.2j

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Abstract:

In this paper, we present the concept of one-parameter pedal unfoldings of a pedal curve in the unit sphere S^2, and we classify their generic singularities with respect to A-equivalence.

Keywords:

spherical pedal curve, pedal unfolding, cross-cap, S_k^± singularity, Chen-Matumoto-Mond singularity, cuspidal edge, cuspidal cross-cap, cuspidal S_k^± singularity, cuspidal Chen-Matumoto-Mond singularity

Mathematical Subject Classification:

58K40, 58K5

Author(s) information:

T. Nishimura
Department of Mathematics
Faculty of Education and Human Sciences
Yokohama National University
Yokohama240-8501, Japan
email: takashi@edhs.ynu.ac.jp