On Kuiper's Question Whether Taut Submanifolds Are Algebraic

Authors

Thomas E. Cecil, College of the Holy CrossFollow
Quo-Shin Chi
Gary Jensen

Document Type

Article

Publication Date

2008

Department

Mathematics

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.

Comments

This is the publisher‘s version of the work. This publication appears in The College of the Holy Cross’ institutional repository by permission of the copyright owner for personal use, not for redistribution.

Originally published in Pacific J. Math. Volume 234, Number 2 (2008), 229-248.

Repository Citation

Cecil, Thomas E.; Quo-Shin Chi and Gary Jensen. On Kuiper's question whether taut submanifolds are algebraic. Pacific J. Math. 234 (2008), no. 2, 229-248.