Harmonic morphisms between Weyl spaces and twistorial maps II
Annales de l'Institut Fourier, Volume 60 (2010) no. 2, p. 433-453

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 a harmonic morphism 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.

Nous définissons, sur les variétés lisses, les notions de structure presque twistorielle et d’application twistorielle, fournissant ainsi un cadre unifié pour tous les exemples d’espace de twisteurs. La condition de morphisme harmonique apparait naturellement dans les propriétés géométriques des applications twistorielles submersives entre espaces de Weyl de faible dimension, équipés d’une structure presque twistorielle non-intégrable due à Eells et Salamon. Ceci mène à la caractérisation twistorielle des morphismes harmoniques entre espaces de Weyl de dimension quatre et trois. De plus, nous donnons une description complète des applications twistorielles à fibres unidimensionelles d’un espace de Weyl de dimension quatre, équipé de la structure presque twistorielle non-intégrable due à Eells et Salamon.

DOI : https://doi.org/10.5802/aif.2528
Classification:  53C43,  53C28
Keywords: Harmonic morphism, Weyl space, twistorial map
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     author = {Loubeau, Eric and Pantilie, Radu},
     title = {Harmonic morphisms between Weyl spaces and twistorial maps II},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {60},
     number = {2},
     year = {2010},
     pages = {433-453},
     doi = {10.5802/aif.2528},
     mrnumber = {2667782},
     zbl = {1203.58005},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2010__60_2_433_0}
}
Loubeau, Eric; Pantilie, Radu. Harmonic morphisms between Weyl spaces and twistorial maps II. Annales de l'Institut Fourier, Volume 60 (2010) no. 2, pp. 433-453. doi : 10.5802/aif.2528. http://www.numdam.org/item/AIF_2010__60_2_433_0/

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