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Harmonic morphisms on conformally flat 3‐spheres
Author(s) -
Heller Sebastian
Publication year - 2011
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdq089
Subject(s) - morphism , mathematics , hopf fibration , fibration , spheres , harmonic , harmonic map , degeneracy (biology) , pure mathematics , mathematical analysis , homotopy , quantum mechanics , physics , astronomy , bioinformatics , biology
We show that under some non‐degeneracy assumptions the only submersive harmonic morphism on a conformally flat 3‐sphere to a surface is the Hopf fibration. The proof involves an appropriate use of the Chern–Simons functional.