Titlebook: Lie Sphere Geometry; With Applications to Thomas E. Cecil Book 19921st edition Springer Science+Business Media New York 1992 Invariant.Lie.

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Springer Science+Business Media New York 1992

GLIB

Lie Sphere Geometry978-1-4757-4096-7Series ISSN 0172-5939 Series E-ISSN 2191-6675

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https://doi.org/10.1007/978-1-4757-4096-7Invariant; Lie; Natural; character; classification; construction; curvature; form; framework; geometry; manifo

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eucalyptus

Book 19921st editionmanifolds. These have recently been classified up to Lie sphere transformation in certain special cases through the introduction of natural Lie invariants. The author provides complete proofs of these classifications and indicates directions for further research and wider application of these methods.

URN

Book 19921st editiongins with Lie‘s construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres and Lie sphere transformation. The link with Euclidean submanifold theory is established via the Legendre map. This provides a powerful framework for the study of

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Introduction,come a valuable tool in the study of Dupin submanifolds in Euclidean space ℝ., beginning with Pinkall’s [1] dissertation in 1981. In this introduction, we will outline the contents of the book and mention some related results.

FLIT

Dupin Submanifolds,rincipal curvatures in ℝ. in Section 4.6. To obtain these classifications, we develop the method of moving Lie frames which can be used in the further study of Dupin submanifolds, or more generally, Legendre submanifolds.