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Classifications Of Dupin Hypersurfaces In Lie Sphere Geometry, Thomas E. Cecil
Classifications Of Dupin Hypersurfaces In Lie Sphere Geometry, Thomas E. Cecil
Mathematics and Computer Science Department Faculty Scholarship
This is a survey of local and global classification results concerning Dupin hypersurfaces in Sn (or Rn) that have been obtained in the context of Lie sphere geometry. The emphasis is on results that relate Dupin hypersurfaces to isoparametric hypersurfaces in spheres. Along with these classification results, many important concepts from Lie sphere geometry, such as curvature spheres, Lie curvatures, and Legendre lifts of submanifolds of Sn (or Rn), are described in detail. The paper also contains several important constructions of Dupin hypersurfaces with certain special properties.
Translation Of: Dupin’Sche Hyperflächen, Doctoral Dissertation, Universität Freiburg (1981) By Ulrich Pinkall, Thomas E. Cecil
Translation Of: Dupin’Sche Hyperflächen, Doctoral Dissertation, Universität Freiburg (1981) By Ulrich Pinkall, Thomas E. Cecil
Mathematics and Computer Science Department Faculty Scholarship
This is an unofficial translation of the original dissertation which was written in German. A few minor typographical errors have been corrected by the translator. All references should be made to the original dissertation. The classification of Dupin hypersurfaces in E4 contained in this dissertation is also contained in the journal article by Ulrich Pinkall, Dupin’sche Hyperflächen in E4, Manuscr. Math. 51 (1985), 89–119.