Reducible Dupin submanifolds |
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| Authors: | Thomas E Cecil |
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| Institution: | (1) Department of Mathematics, College of the Holy Cross, 01610 Worcester, MA, U.S.A. |
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| Abstract: | Pinkall's standard constructions for obtaining a Dupin hypersurface W in 
N
from a Dupin hypersurface M in
n
, N>n, are studied in the context of Lie sphere geometry. It is shown that a compact Dupin hypersurface W in
N
with g distinct principal curvatures at each point is reducible to a compact Dupin hypersurface M in
n
if and only if g=2.This research was supported by NSF Grant No. DMS 87-06015. |
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| Keywords: | |
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