Lie Sphere Geometry

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 Spacelike Vector Proper Point Point Sphere 
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© Springer Science+Business Media, LLC 2008

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