An affine analogue of the Hartman-Nirenberg cylinder theorem
| dc.creator | Akivis, Maks A. | |
| dc.creator | Goldberg, Vladislav V. | |
| dc.date | 2000-09-24 | |
| dc.date | 2001-05-30 | |
| dc.date.accessioned | 2026-07-07T04:37:40Z | |
| dc.date.available | 2026-07-07T04:37:40Z | |
| dc.description | Let X be a smooth, complete, connected submanifold of dimension n < N in a complex affine space A^N (C), and r is the rank of its Gauss map γ, γ(x) = T_x (X). The authors prove that if 2 \leq r \leq n - 1, N - n \geq 2, and in the pencil of the second fundamental forms of X, there are two forms defining a regular pencil all eigenvalues of which are distinct, then the submanifold X is a cylinder with (n-r)-dimensional plane generators erected over a smooth, complete, connected submanifold Y of rank r and dimension r. This result is an affine analogue of the Hartman-Nirenberg cylinder theorem proved for X \subset R^{n+1} and r = 1. For n \geq 4 and r = n - 1, there exist complete connected submanifolds X \subset A^N (C) that are not cylinders. | |
| dc.description | AMS-LaTeX, 9 pages; revised version (the main theorem refined, and its conditions are given in terms of the second fundamental form of a variety in question) | |
| dc.identifier | https://arxiv.org/abs/math/0009211 | |
| dc.identifier | http://arxiv.org/abs/math/0009211 | |
| dc.identifier | Math. Ann., 322 (2002) no. 3 573-582 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59989 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53A15 (Primary), 53A05, 53A20 (Secondary) | |
| dc.title | An affine analogue of the Hartman-Nirenberg cylinder theorem | |
| dc.type | text |