2014/05/20 by Gary R. Jensen, Jensen, Gary R.
Mathematics · #53A30 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A30 #msc:53C42
paper · pdf · doi:10.48550/arxiv.1405.5198
To appear in the Shoshichi Kobayashi Memorial Volume of Progress in Mathematics, Birkhauser
arxiv created 2014/05/20 · arxiv updated 2014/05/21
The method of moving frames in Lie sphere geometry has produced significant results in the classification of Dupin hypersurfaces in spheres. What is the secret of its effectiveness? The answer emerges in the classification of nonumbilic isoparametric surfaces in the space form geometries. Using the method of moving frames, the proof of this classification is an elementary exercise. The same proof classifies the cyclides of Dupin in Möbius geometry and finally in Lie sphere geometry, where all nonumbilic Dupin immersions are Lie sphere congruent to each other.