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Line Geometry, Sphere Geometry, Kinematics

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Abstract

A Dupin cyclide is a quartic and cyclic surface. It is the envelope of a one parameter family of spheres. In Lie’s model of sphere geometry, it is represented by a conic. Lie’s line-sphere-mapping maps a conic in Lie’s quadric to a conic on Plücker’s quadric which corresponds to a regulus in the manifold of lines. Each regulus defines a ruled quadric, for example, a one-sheeted hyperboloid. Consequently, up to Lie’s line-sphere-mapping, there is no difference between a Dupin cyclide and a ruled quadric.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Department of GeometryUniversity of Applied Arts ViennaViennaAustria
  2. 2.Institute of Discrete Mathematics and GeometryVienna University of TechnologyViennaAustria
  3. 3.Department of GeometryUniversity of Applied Arts ViennaViennaAustria

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