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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Harmonic morphisms with one-dimensional fibres on Einstein manifolds
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by Radu Pantilie and John C. Wood PDF
Trans. Amer. Math. Soc. 354 (2002), 4229-4243 Request permission

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
  • 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.
  • © Copyright 2002 American Mathematical Society
  • 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
  • MathSciNet review: 1926872