Harmonic morphisms on conformally flat 3-spheres

Details Harmonic morphisms on conformally flat 3-spheres Harmonic morphisms on conformally flat 3-spheres

2009-02-26

arxiv.org/abs/0902.4558v1

Mathematics

Differential Geometry

14 pages, Part of authors PhD thesis

Scientific paper

We show that under some non-degeneracy assumption the only submersive
harmonic morphism on a conformally flat $3-$sphere is the Hopf fibration. The
proof involves an appropriate use the Chern-Simons functional.

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