Maps That Take Lines to Circles, in Dimension 4

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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.
10 pages

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Differential Geometry, Metric Geometry, 53A04

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http://salesiana.dossiersoluciones.com/handle/123456789/68457

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0309053
 http://arxiv.org/abs/math/0309053

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arXiv