On Rectification of Circles and an Extension of Beltrami's Theorem
| dc.creator | Izadi, Farzali | |
| dc.date | 2003-01-20 | |
| dc.date.accessioned | 2026-07-07T04:54:34Z | |
| dc.date.available | 2026-07-07T04:54:34Z | |
| dc.description | The goal of this paper is to describe all local diffeomorphisms mapping a family of circles, in an open subset of $\r^3$, into straight lines. This paper contains two main results. The first is a complete description of the rectifiable collection of circles in $\r^3$ passing through one point. It turns out that to be rectifiable all circles need to pass through some other common point. The second main result is a complete description of geometries in $\r^3$ in which all the geodesics are circles. This is a consequence of an extension of Beltrami's theorem by replacing straight lines with circles.} | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/math/0301220 | |
| dc.identifier | http://arxiv.org/abs/math/0301220 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66302 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53A04; 53B20 | |
| dc.title | On Rectification of Circles and an Extension of Beltrami's Theorem | |
| dc.type | text |