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.
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© 1992 Springer Science+Business Media New York
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Cecil, T.E. (1992). Lie Sphere Geometry. In: Lie Sphere Geometry. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4096-7_2
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DOI: https://doi.org/10.1007/978-1-4757-4096-7_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97747-8
Online ISBN: 978-1-4757-4096-7
eBook Packages: Springer Book Archive