Vol. 234, No. 2, 2008
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On Kuiper's question whether taut submanifolds are algebraic

Thomas E. Cecil & Quo-Shin Chi & Gary R. Jensen

Vol. 234 (2008), No. 2, 229-247
Abstract

We prove that any connected proper Dupin hypersurface in Rn is analytic algebraic and is an open subset of a connected component of an irreducible algebraic set. From this we also prove that every taut submanifold of dimension m ≤ 4 is algebraic by exploring a finiteness condition.
Keywords

Dupin hypersurface, taut submanifold, semialgebraic set

Mathematical Subject Classification

Primary: 53C40, 53C42
Authors
Thomas E. Cecil
Department of Mathematics and Computer Science
College of the Holy Cross
Worcester, MA 01610-2395
United States
Quo-Shin Chi
Department of Mathematics
Campus Box 1146
Washington University
St. Louis, MO 63130
United States
Gary R. Jensen
Department of Mathematics
Campus Box 1146
Washington University
St. Louis, MO 63130
United States