Harmonic morphisms with one-dimensional fibres on conformally-flat Riemannian manifolds

• Autores: Radu Pantilie
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 145, Nº 1, 2008, págs. 141-152
• Idioma: inglés
• DOI: 10.1017/s0305004108001060
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• Resumen

  • We classify the harmonic morphisms with one-dimensional fibres (1) from real-analytic conformally-flat Riemannian manifolds of dimension at least four (Theorem 3.1), and (2) between conformally-flat Riemannian manifolds of dimensions at least three (Corollaries 3.4 and 3.6).

    Also, we prove (Proposition 2.5) an integrability result for any real-analytic submersion, from a constant curvature Riemannian manifold of dimension n+2 to a Riemannian manifold of dimension 2, which can be factorised as an n-harmonic morphism with two-dimensional fibres, to a conformally-flat Riemannian manifold, followed by a horizontally conformal submersion, (n=4).