Compatible Complex Structures on Twistor Spaces

Let (M,g) be a Riemannian 4-manifold. The twistor space Z->M is a CP1-bundle whose total space Z admits a natural metric h. The aim of this article is to study properties of complex structures on (Z,h) which are compatible with the CP1-fibration and the metric h. The results obtained enable us to translate some metric properties on M in terms of complex properties on its twistor space Z.Comment: 23 page

Espaces twistoriels et structures complexes non standards

In this article we use the twistor theory in order to build "non standard" complex structures (with a meaning which we define) on the products of 4-manifolds with the sphere of dimension two. To that end, we enumerate the set of complex surfaces whose twistor space is C∞-trivial. Among these surface we will study those which admit an anti-self-dual riemannian metric

Feuilletage lisse de S5S^5 par surfaces complexes

In 2002 Meersseman-Verjovsky [2] constructed a smooth, codimension-one, foliation on 5-sphere by complex surfaces with two compact leaves. The aim of this note is to improve their construction in order to give a smooth foliation on 5-sphere by complex surfaces with only one compact leaf

Divination en Gaule du IVe au VIe siècle : études de cas

Ce mémoire porte sur la continuité des rituels divinatoires païens dans le cadre du culte chrétien en Gaule du IVe au VIe siècle. Il comporte une introduction rapportant notre problématique, notre terminologie, notre méthodologie ainsi que nos sources principales. Par la suite, le développement aborde les rites divinatoires des Sortes Sanctorum, des Sortes Sangallenses et les rites d’incubation dans le culte de Saint Martin de Tours. Pour chacun de ces cas, nous étudions leur provenance, leurs sources, leur déroulement, leur évolution et les similarités qui permettent de faire un lien avec des rituels païens déjà existants. Nous avons vérifié l’existence de cette continuité et déterminé qu’elle passait par plusieurs phénomènes, l’acculturation gauloise des rituels gréco-romains, l’importation de rites christianisés en Orient et l’assimilation des pratiques païennes locales par le culte chrétien pour répondre à une demande de divination par la population.This Masters’ thesis concerns itself with the continuity of pagan divination rituals within the new context of the Christianized Gaul of the IVth to VIth centuries. It is composed of an introduction detailing our hypothesis, terminology, methodology and sources. Afterwards, we study three cases of divination rituals, the Sortes Sanctorum, the Sortes Sangallenses and the incubations within the cult of St. Martin of Tours. We detail their origins, sources, proceedings, evolution and the similarities linking them to previously existing pagan rites. In conclusion, we synthesize all elements and we were able to draw from our cases to establish the continuity of these rituals by several means, the Gallic acculturation of Greco-Roman rituals, importation of Christianized rituals from the East of the Empire and assimilation of local pagan practices within the Christian religion to answer the popular demand for divination

Espaces twistoriels et structures complexes non standards.

In this paper we use the twistor theory in order to build non standard complex structures (with a meaning which we define) on products of 4-manifolds with the sphere of dimension two. To that end, we enumerate the set of complex surfaces whose twistor space is topologically trivial. Among these surfaces, we determine those which admit a spin structure or an anti-selfdual riemannian metric

Hessian of the natural Hermitian form on twistor spaces

We compute the hessian of the natural Hermitian form successively on the Calabi family of a hyperk\"ahler manifold, on the twistor space of a 4-dimensional anti-self-dual Riemannian manifold and on the twistor space of a quaternionic K\"ahler manifold. We show a strong convexity property of the cycle space of twistor lines on the Calabi family of a hyperk\"ahler manifold. We also prove convexity properties of the 1-cycle space of the twistor space of a 4-dimensional anti-self-dual Einstein manifold of non-positive scalar curvature and of the 1-cycle space of the twistor space of a quaternionic K\"ahler manifold of non-positive scalar curvature. We check that no non-K\"ahler strong KT manifold occurs as such a twistor space