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Harmonic morphisms with one-dimensional fibres on Einstein manifolds


Authors: Radu Pantilie and John C. Wood
Journal: Trans. Amer. Math. Soc. 354 (2002), 4229-4243
MSC (2000): Primary 58E20; Secondary 53C43
DOI: https://doi.org/10.1090/S0002-9947-02-03044-1
Published electronically: May 22, 2002
MathSciNet review: 1926872
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Abstract: We prove that, from an Einstein manifold of dimension greater than or equal to five, there are just two types of harmonic morphism with one-dimensional fibres. This generalizes a result of R.L. Bryant who obtained the same conclusion under the assumption that the domain has constant curvature.


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Additional Information

Radu Pantilie
Affiliation: School of Mathematics, University of Leeds, Leeds LS2 9JT, England
Email: r.pantilie@leeds.ac.uk

John C. Wood
Affiliation: School of Mathematics, University of Leeds, Leeds LS2 9JT, England
Email: j.c.wood@leeds.ac.uk\,.

DOI: https://doi.org/10.1090/S0002-9947-02-03044-1
Keywords: Harmonic morphism, foliation, Einstein manifold
Received by editor(s): December 17, 2001
Published electronically: May 22, 2002
Additional Notes: The authors gratefully acknowledge that this work was done under E.P.S.R.C. grant number GR/N27897.
Article copyright: © Copyright 2002 American Mathematical Society

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