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2. Espaces twistoriels et structures complexes non standards

Author

Guillaume Deschamps, Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), and Deschamps, Guillaume

Subjects
Pure mathematics, métrique anti-autoduale, Spin structure, General Mathematics, structure spin, Fundamental theorem of Riemannian geometry, Twistor space, 01 natural sciences, parallelisable complex surface, Twistor theory, High Energy Physics::Theory, self-dual metric, almost hypercomplex manifold, Almost hypercomplex manifold, classification de Kodaira, 0103 physical sciences, 51M99, Hermitian manifold, 0101 mathematics, Mathematics, Enriques-Kodaira classification, 010102 general mathematics, Mathematical analysis, [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV], Surface (topology), Fubini–Study metric, spin structure, Self-dual metric, 53C27, 53C28, [MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV], 010307 mathematical physics, Enriques–Kodaira classification, Mathematics::Differential Geometry, Parallelisable complex surface, Espace twistoriel, Fisher information metric
Abstract

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.

Published
2006

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