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Bulletin of the London Mathematical Society Advance Access originally published online on March 11, 2009
Bulletin of the London Mathematical Society 2009 41(2):198-204; doi:10.1112/blms/bdp006
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© 2009 London Mathematical Society

Harmonic morphisms on heaven spaces

Paul Baird

Département de Mathématiques
Laboratoire C.N.R.S. U.M.R. 6205
Université de Bretagne Occidentale
6, Avenue Victor Le Gorgeu
CS 93837
29238 Brest Cedex 3
France

Radu Pantilie

Institutul de Matematica ‘Simion Stoilow’ al Academiei Române
C.P. 1-764
014700
Bucuresti
România
Radu.Pantilie@imar.ro

Received 10 October 2007. Revision received 23 October 2008.

We prove that any (real or complex) analytic horizontally conformal submersion from a three-dimensional conformal manifold (M3, cM) to a two-dimensional conformal manifold (N2, cN) can be, locally, ‘extended’ to a unique harmonic morphism from the H(eaven)-space (H4, g) of (M3, cN) to (N2, cN). Moreover, any positive harmonic morphism with two-dimensional fibres from (H4, g) is obtained in this way.

2000 Mathematics Subject Classification 53C43 (primary), 53C28 (secondary).

The second author was partially supported by the CNCSIS grant, code 811, and by a PN II IDEI grant, code 1193.


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