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Normal forms for singularities of pedal curves produced by non-singular dual curve germs in S n

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Abstract

For an n-dimensional spherical unit speed curve r and a given point P, we can define naturally the pedal curve of r relative to the pedal point P. When the dual curve germs are non-singular, singularity types of such pedal curves depend only on locations of pedal points. In this paper, we give a complete list of normal forms for singularities and locations of pedal points when the dual curve germs are non-singular. As an application of our list, we characterize C ∞ left equivalence classes of pedal curve germs (I, s 0) → S n produced by non-singular dual curve germ from the viewpoint of the relation between \({\mathcal{L}}\) tangent space and \({\mathcal{C}}\) tangent space.

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  1. Department of Mathematics, Faculty of Education and Human Sciences, Yokohama National University, Yokohama, 240-8501, Japan

    Takashi Nishimura

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  1. Takashi Nishimura
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Correspondence to Takashi Nishimura.

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Nishimura, T. Normal forms for singularities of pedal curves produced by non-singular dual curve germs in S n . Geom Dedicata 133, 59–66 (2008). https://doi.org/10.1007/s10711-008-9233-5

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  • DOI: https://doi.org/10.1007/s10711-008-9233-5

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