Rectification of circles and quaternions
Differential Geometry
2007-05-23 v1 Metric Geometry
Abstract
Consider a bundle of circles passing through 0 in 4-dimensional space. It is said to be rectifiable if there is a germ of diffeomorphism at 0 that takes all circles from our bundle to straight lines. We will give a classification of all rectifiable bundles of circles containing sufficiently many circles in general position. This result is surprisingly different from those in dimensions 2 and 3(Khovanskii and Izadi) due to a connection with the quaternionic algebra.
Cite
@article{arxiv.math/0110144,
title = {Rectification of circles and quaternions},
author = {Vladlen Timorin},
journal= {arXiv preprint arXiv:math/0110144},
year = {2007}
}
Comments
18 pages