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On Kuiper’s question
whether taut submanifolds are algebraic
Thomas E. Cecil, Quo-Shin Chi and Gary R. Jensen |
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Vol. 234 (2008), No. 2, 229–247
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Abstract |
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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
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Mathematical Subject Classification 2000
Primary: 53C40, 53C42
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Milestones
Received: 16 March 2007
Revised: 10 December 2007
Accepted: 14 December 2007
Published: 1 February 2008
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Authors |
| Thomas E. Cecil | |
| Department of Mathematics and
Computer Science College of the Holy Cross Worcester, MA 01610-2395 United States |
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| Quo-Shin Chi | |
| Department of Mathematics Campus Box 1146 Washington University St. Louis, MO 63130 United States |
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| Gary R. Jensen | |
| Department of Mathematics Campus Box 1146 Washington University St. Louis, MO 63130 United States |
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