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Singular fibres of harmonic morphisms on S4

Abstract : In this paper, we study the singular minimal foliation by the fibres of harmonic morphisms due to Burel from into where is a family of conformal metrics on . The map arises from a composition of a map to followed by a mapping of Hopf invariant kl. Regular fibres determine a foliation by minimal surfaces which becomes singular at critical points. In order to study the singular set we introduce a notion of multiple fibre and apply 4-dimensional intersection theory.
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Submitted on : Monday, October 25, 2021 - 4:33:51 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:12 PM

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Ali Makki, Marc Soret, Marina Ville. Singular fibres of harmonic morphisms on S4. Differential Geometry and its Applications, Elsevier, 2019, 67, pp.101550. ⟨10.1016/j.difgeo.2019.06.006⟩. ⟨hal-02342149⟩

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