Lie Sphere Geometry

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


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.


Bijective Correspondence Lightlike Vector Proper Point Point Sphere Real Vector Space Versus 
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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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