Hyperbolic Carathéodory conjecture
| dc.creator | Ovsienko, Valentin | |
| dc.creator | Tabachnikov, Serge | |
| dc.date | 2006-11-21 | |
| dc.date.accessioned | 2026-07-07T07:33:10Z | |
| dc.date.available | 2026-07-07T07:33:10Z | |
| dc.description | A quadratic point on a surface in $RP^3$ is a point at which the surface can be approximated by a quadric abnormally well (up to order 3). We conjecture that the least number of quadratic points on a generic compact non-degenerate hyperbolic surface is 8; the relation between this and the classic Carathéodory conjecture is similar to the relation between the six-vertex and the four-vertex theorems on plane curves. Examples of quartic perturbations of the standard hyperboloid confirm our conjecture. Our main result is a linearization and reformulation of the problem in the framework of 2-dimensional Sturm theory; we also define a signature of a quadratic point and calculate local normal forms recovering and generalizing Tresse-Wilczynski's theorem. | |
| dc.description | Latex 25 pages, 10 figures | |
| dc.identifier | https://arxiv.org/abs/math/0611630 | |
| dc.identifier | http://arxiv.org/abs/math/0611630 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119363 | |
| dc.subject | Differential Geometry | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 53A20, 53C99, 58K50 | |
| dc.title | Hyperbolic Carathéodory conjecture | |
| dc.type | text |