Maps That Take Lines to Circles, in Dimension 4

Details Maps That Take Lines to Circles, in Dimension 4 Maps That Take Lines to Circles, in Dimension 4

2003-09-03

arxiv.org/abs/math/0309053v1

Mathematics

Differential Geometry

10 pages

Scientific paper

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.

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