Harmonic morphisms between Weyl spaces and twistorial maps II

Details Harmonic morphisms between Weyl spaces and twistorial maps II Harmonic morphisms between Weyl spaces and twistorial maps II

2006-10-23

arxiv.org/abs/math/0610676v3

Mathematics

Differential Geometry

minor corrections

Scientific paper

We define, on smooth manifolds, the notions of almost twistorial structure and twistorial map, thus providing a unified framework for all known examples of twistor spaces. The condition of being harmonic morphisms naturally appears among the geometric properties of submersive twistorial maps between low-dimensional Weyl spaces endowed with a nonintegrable almost twistorial structure due to Eells and Salamon. This leads to the twistorial characterisation of harmonic morphisms between Weyl spaces of dimensions four and three. Also, we give a thorough description of the twistorial maps with one-dimensional fibres from four-dimensional Weyl spaces endowed with the almost twistorial structure of Eells and Salamon.

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