Maps That Take Lines to Circles, in Dimension 4
Differential Geometry
2007-05-23 v1 Metric Geometry
Abstract
We list all analytic diffeomorphisms between an open subset of the 4-dimensional projective space and an open subset of the 4-dimensional sphere that take all line segments to arcs of round circles. These are the following: restrictions of the quaternionic Hopf fibrations and projections from a hyperplane to a sphere from some point. We prove this by finding the exact solutions of the corresponding system of partial differential equations.
Cite
@article{arxiv.math/0309053,
title = {Maps That Take Lines to Circles, in Dimension 4},
author = {Vladlen Timorin},
journal= {arXiv preprint arXiv:math/0309053},
year = {2007}
}
Comments
10 pages