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


Lie [1] introduced his geometry of oriented spheres in his dissertation, published as a paper in Mathematische Annalen in 1872. Sphere geometry was also prominent in his study of contact transformations (Lie-Scheffers [1]) and in Volume III of Blaschke’s [1] Vorlesungen über Differentialgeometrie, published in 1929. In recent years, sphere geometry has become a valuable tool in the study of Dupin submanifolds in Euclidean space ℝn, beginning with Pinkall’s [1] dissertation in 1981. In this introduction, we will outline the contents of the book and mention some related results.


Principal Curvature Sphere Geometry Isoparametric Hypersurface Contact Transformation Distinct Principal Curvature 
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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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