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Evolutes of Hyperbolic Plane Curves 被引量:2

Evolutes of Hyperbolic Plane Curves
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摘要 We define the notion of evolutes of curves in a hyperbolic plane and establish the relation-ships between singularities of these subjects and geometric invariants of curves under the action of theLorentz group.We also describe how we can draw the picture of an evolute of a hyperbolic plane curvein the Poincaré disk. 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.
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2004年第3期543-550,共8页 数学学报(英文版)
关键词 Evolute Generic property Hyperbolic plane curve Evolute Generic property Hyperbolic plane curve
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参考文献3

  • 1Bruce, J, W., Giblin, P. J,: Curves and singularities (second edition), Cambridge University Press, Glasgow,1992.
  • 2Torii, E.: On curves on the hyperboloid or the pseudo-sphere in Minkowski 3-space, Master thesis of Hokkaido University, 1999 (in Japanese).
  • 3O'Neill, B.: Semi-Riemannian Geometry, Academic Press, New York, 1983.

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