. D G ] 3 S ep 2 00 3 Maps That Take Lines to Circles , in Dimension 4
نویسنده
چکیده
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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