Dupin Submanifolds

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

Abstract

In this chapter, we concentrate on local results which have been obtained using Lie sphere geometry. The main results are the classification of proper Dupin submanifolds with two principal curvatures (cyclides of Dupin) in Section 4.3 and the classification of proper Dupin hypersurfaces with three principal curvatures in ℝ4 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.

Keywords

Principal Curvature Isoparametric Hypersurface Distinct Principal Curvature Curvature Sphere Euclidean Projection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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