Lie Sphere Geometry in $\mathbf R^3$

Volume 117 / 2019

Gary R. Jensen Banach Center Publications 117 (2019), 211-222 MSC: Primary 53A40; Secondary 53-02, 53A30, 53B25. DOI: 10.4064/bc117-7


These notes introduce Lie sphere geometry of surfaces in Euclidean 3-space. A similar article with a different point of view is: G. R. Jensen, Dupin hypersurfaces in Lie sphere geometry, in: Geometry and Analysis on Manifolds, Progr. Math. 308, Birkhäuser/Springer, Cham, 2015, 383–394. More details are in the book: G. R. Jensen, E. Musso, L. Nicolodi, Surfaces in Classical Geometries, Universitext, Springer, Cham, 2016, Chapter 15. An exposition of Lie sphere geometry in all dimensions is in: Th. E. Cecil, Lie Sphere Geometry, Universitext, Springer, New York, 2008.


  • Gary R. JensenDepartment of Mathematics
    Washington University
    Campus Box 1146
    One Brookings Drive
    St. Louis, MO 63130

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