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 2000

Primary: 53C40, 53C42

Milestones

Received: 16 March 2007
Revised: 10 December 2007
Accepted: 14 December 2007

Authors