Harmonic morphisms on conformally flat 3-spheres
Sebastian Heller
TL;DR
This paper proves that, under certain conditions, the only harmonic morphism from a conformally flat 3-sphere is the Hopf fibration, using the Chern-Simons functional in the proof.
Contribution
It establishes a uniqueness result for harmonic morphisms on conformally flat 3-spheres, identifying the Hopf fibration as the sole example under specific assumptions.
Findings
The Hopf fibration is the unique submersive harmonic morphism on conformally flat 3-spheres under certain conditions.
The proof utilizes the Chern-Simons functional to establish the result.
The result characterizes harmonic morphisms in a geometric setting of conformally flat 3-spheres.
Abstract
We show that under some non-degeneracy assumption the only submersive harmonic morphism on a conformally flat sphere is the Hopf fibration. The proof involves an appropriate use the Chern-Simons functional.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Geometric and Algebraic Topology