Diffeomorphisms taking lines to circles, and quaternionic Hopf fibrations |
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| Authors: | V. A. Timorin |
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| Affiliation: | (1) Independent University of Moscow, Russia;(2) Institute for Mathematical Sciences, State University of New York at Stony Brook, USA |
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| Abstract: | We list all diffeomorphisms between an open subset of the four-dimensional projective space and an open subset of the four-dimensional sphere that take all line segments to arcs of round circles. These diffeomorphisms are restrictions of quaternionic Hopf fibrations and radial projections from hyperplanes to spheres. |
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| Keywords: | line circle quaternionic Hopf fibration |
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