On the geometry of harmonic morphisms. (English) Zbl 0715.53029

Gudmundsson, Sigmundur

Math. Proc. Camb. Philos. Soc. 108, No. 3, 461-466 (1990).

Author’s abstract: “Let \(\pi\) : \(M\to B\) 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.”

Reviewer: J.Szilasi

MSC:

53C12	Foliations (differential geometric aspects)
58E20	Harmonic maps, etc.
53A30	Conformal differential geometry (MSC2010)

Keywords:

conformal submersion; curvature conditions; conformal maps; harmonic morphisms

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