%0 Journal Article
%T On Rectification of Circles and an Extension of Beltrami's Theorem
%A Farzali Izadi
%J Mathematics
%D 2003
%I arXiv
%X 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.}
%U http://arxiv.org/abs/math/0301220v1