Line Geometry, Sphere Geometry, Kinematics

Boris Odehnal (), Hellmuth Stachel () and Georg Glaeser ()
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Boris Odehnal: University of Applied Arts Vienna, Department of Geometry
Hellmuth Stachel: Vienna University of Technology, Institute of Discrete Mathematics and Geometry
Georg Glaeser: University of Applied Arts Vienna, Department of Geometry

Chapter Chapter 10 in The Universe of Quadrics, 2020, pp 475-559 from Springer

Abstract: 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.

Date: 2020
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DOI: 10.1007/978-3-662-61053-4_10

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