On the geometry of harmonic morphisms

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Abstract

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.

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  • Mathematics
Original languageEnglish
Pages (from-to)461-466
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume108
Issue number3
Publication statusPublished - 1990
Publication categoryResearch
Peer-reviewedYes