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Holomorphic harmonic morphisms from four-dimensional non-Einstein manifolds

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Author

Summary, in English

We construct 4-dimensional Riemannian Lie groups carrying left-invariant conformal foliations with minimal leaves of codimension 2. We show that these foliations are holomorphic with respect to an (integrable) Hermitian structure which is not Kähler. We then prove that the Riemannian Lie groups constructed are not Einstein manifolds. This answers an important open question in the theory of complex-valued harmonic morphisms from Riemannian 4-manifolds.

Department/s

Publishing year

2015

Language

English

Publication/Series

International Journal of Mathematics

Volume

26

Issue

1

Document type

Journal article

Publisher

World Scientific Publishing

Topic

  • Geometry

Keywords

  • harmonic morphisms
  • holomorphic foliations
  • Einstein manifolds

Status

Published

Research group

  • Differential Geometry

ISBN/ISSN/Other

  • ISSN: 0129-167X