On the geometry of harmonic morphisms

Summary, in English

Let π:M→B be a horizontally conformal submersion. We give necessary curvature conditions on the manifolds M and B, which lead to non-existence results for certain horizontally conformal maps, and harmonic morphisms. We then classify all such maps between open subsets of Euclidean spaces, which additionally have totally geodesic fibres and are horizontally homothetic. They are orthogonal projections on each connected component, followed by a homothety.

• Författare: Sigmundur Gudmundsson
• Avdelning/ar: Differential Geometry
• Publiceringsår: 1990
• Språk: Engelska
• Sidor: 461-466
• Publikation/Tidskrift/Serie: Mathematical Proceedings of the Cambridge Philosophical Society
• Volym: 108
• Issue: 3
• Länkar: http://journals.cambridge.org/download.php?file=%2FPSP%2FPSP108_03%2FS0305004100069358a.pdf&code=56018985e812666e91f4e05f6aebbcf2; http://dx.doi.org/10.1017/S0305004100069358
• Dokumenttyp: Artikel i tidskrift
• Förlag: Cambridge University Press
• Ämne: Geometry
• Status: Published
• Forskningsgrupp: Differential Geometry
• ISBN/ISSN/Övrigt: ISSN: 1469-8064