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Evolutes of Hyperbolic Plane Curves

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Abstract

We define the notion of evolutes of curves in a hyperbolic plane and establish the relationships between singularities of these subjects and geometric invariants of curves under the action of the Lorentz group. We also describe how we can draw the picture of an evolute of a hyperbolic plane curve in the Poincaré disk.

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References

  1. Bruce, J. W., Giblin, P. J.: Curves and singularities (second edition), Cambridge University Press, Glasgow, 1992

  2. Torii, E.: On curves on the hyperboloid or the pseudo-sphere in Minkowski 3-space, Master thesis of Hokkaido University, 1999 (in Japanese)

  3. O'Neill, B.: Semi-Riemannian Geometry, Academic Press, New York, 1983

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo, 060-0810, Japan

    Shyuichi Izumiya

  2. Department of Mathematics, North East Normal University, Changchun, 130024, P. R. China

    Dong He Pei

  3. Faculty of Engineering, Hokkai-Gakuen University, Sapporo, 062-8605, Japan

    Takashi Sano

  4. Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo, 060-0810, Japan

    Erika Torii

Authors
  1. Shyuichi Izumiya
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  2. Dong He Pei
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  3. Takashi Sano
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  4. Erika Torii
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Correspondence to Shyuichi Izumiya.

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Izumiya, S., Pei, D.H., Sano, T. et al. Evolutes of Hyperbolic Plane Curves. Acta Math Sinica 20, 543–550 (2004). https://doi.org/10.1007/s10114-004-0301-y

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  • DOI: https://doi.org/10.1007/s10114-004-0301-y

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