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Zbl 1203.58005
Loubeau, Eric; Pantilie, Radu
Harmonic morphisms between Weyl spaces and twistorial maps. II. (English)
[J] Ann. Inst. Fourier 60, No. 2, 433-453 (2010). ISSN 0373-0956; ISSN 1777-5310/e

The authors define an almost twistorial structure on a smooth manifold to be a locally trivial fibre space over that manifold, equipped with a complex distribution which induces almost complex structures on each fibre. This notion provides a unified framework for all known examples of twistor spaces. In the smooth category, a twistor on a manifold $M$ is a pair consisting of an immersed submanifold and a linear CR-structure on its normal bundle. \par The paper contains twistorial characterisations of harmonic morphisms between Weyl spaces of dimensions $4$ and $3$. Moreover, the authors describe the twistorial maps with $1$-dimensional fibres from $4 $-dimensional Weyl spaces endowed with the almost twistorial structure of [{\it J. Eells} and {\it S. Salamon}, Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 12, 589--640 (1985; Zbl 0627.58019)]. [For Part I, cf. {\it E. Loubeau} and {\it R. Pantile}, Commun. Anal. Geom. 14, No. 5, 847--881 (2006; Zbl 1127.58010).]
[Andreas Gastel (Duisburg)]

MSC 2000:: *58E20 Harmonic maps between infinite-dimensional spaces
53C43 Differential geometric aspects of harmonic maps
53C28 Twistor methods

Keywords: harmonic morphism; Weyl space; twistorial map

Citations: Zbl 0627.58019; Zbl 1127.58010

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