On Kuiper's conjecture
| dc.creator | Cecil, Thomas | |
| dc.creator | Chi, Quo-Shin | |
| dc.creator | Jensen, Gary | |
| dc.date | 2005-12-05 | |
| dc.date | 2007-07-31 | |
| dc.date.accessioned | 2026-07-07T08:21:11Z | |
| dc.date.available | 2026-07-07T08:21:11Z | |
| dc.description | We prove that any connected proper Dupin hypersurface in $\R^n$ is analytic algebraic and is an open subset of a connected component of an irreducible algebraic set. We prove the same result for any connected non-proper Dupin hypersurface in $\R^n$ that satisfies a certain finiteness condition. Hence any taut submanifold M in $\R^n$, whose tube $M_ε$ satisfies this finiteness condition, is analytic algebraic and is a connected component of an irreducible algebraic set. In particular, we prove that every taut submanifold of dimension $m \leq 4$ is algebraic. | |
| dc.description | 43 pages | |
| dc.identifier | https://arxiv.org/abs/math/0512089 | |
| dc.identifier | http://arxiv.org/abs/math/0512089 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135280 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C40 | |
| dc.title | On Kuiper's conjecture | |
| dc.type | text |