Lie Sphere Geometry

  • Thomas E. Cecil
Part of the Universitext book series (UTX)

Abstract

In this chapter, we give Lie’s construction of the space of spheres and define the important notions of oriented contact and parabolic pencils of spheres. This leads ultimately to a bijective correspondence between the manifold of contact elements on the sphere S n and the manifold Λ2n−1 of projective lines on the Lie quadric.

Keywords

Bijective Correspondence Lightlike Vector Proper Point Point Sphere Real Vector Space Versus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Thomas E. Cecil
    • 1
  1. 1.Department of MathematicsCollege of the Holy CrossWorcesterUSA

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