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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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Contributor : Marina Ville <>
Submitted on : Thursday, October 31, 2019 - 5:22:52 PM
Last modification on : Monday, December 14, 2020 - 7:48:01 PM




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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