Evolutes of Hyperbolic Plane Curves
Acta Mathematica Sinica, English Series
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Acta Mathematica Sinica, English Series  2004, Vol. 20 Issue (3): 543-550    DOI: 10.1007/s10114-004-0301-y
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Evolutes of Hyperbolic Plane Curves
Shyuichi IZUMIYA1, Dong He PEI2, Takashi SANO3, Erika TORII1
1. Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo, 060-0810, Japan;
2. Department of Mathematics, North East Normal University, Changchun, 130024, P. R. China;
3. Faculty of Engineering, Hokkai-Gakuen University, Sapporo, 062-8605, Japan
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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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Shyuichi IZUMIYA
Dong He PEI
Takashi SANO
Erika TORII
Key wordsEvolute   Generic property   Hyperbolic plane curve     
Received: 2001-02-20;
Cite this article:   
Shyuichi IZUMIYA,Dong He PEI,Takashi SANO et al. Evolutes of Hyperbolic Plane Curves[J]. Acta Mathematica Sinica, English Series, 2004, 20(3): 543-550.
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http://www.actamath.com/Jwk_sxxb_en//EN/10.1007/s10114-004-0301-y      or     http://www.actamath.com/Jwk_sxxb_en//EN/Y2004/V20/I3/543
 
[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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