Circles and Quadratic Maps Between Spheres
| dc.creator | Timorin, Vladlen | |
| dc.date | 2002-12-06 | |
| dc.date | 2004-12-11 | |
| dc.date.accessioned | 2026-07-07T04:53:36Z | |
| dc.date.available | 2026-07-07T04:53:36Z | |
| dc.description | Consider an analytic map of a neighborhood of 0 in a vector space to a Euclidean space. Suppose that this map takes all germs of lines passing through 0 to germs of circles. Such a map is called rounding. We introduce a natural equivalence relation on roundings and prove that any rounding, whose differential at 0 has rank at least 2, is equivalent to a fractional quadratic rounding. A fractional quadratic map is just the ratio of a quadratic map and a quadratic polynomial. We also show that any rounding gives rise to a quadratic map between spheres. The known results on quadratic maps between spheres have some interesting implications concerning roundings. | |
| dc.description | 14 pages, v3: minor changes to improve readability | |
| dc.identifier | https://arxiv.org/abs/math/0212098 | |
| dc.identifier | http://arxiv.org/abs/math/0212098 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65911 | |
| dc.subject | Metric Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | 15A63 | |
| dc.title | Circles and Quadratic Maps Between Spheres | |
| dc.type | text |