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Espaces twistoriels et structures complexes exotiques

Abstract : In this thesis 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 an antiselfdual riemannian metric. From these results, we deduce a simple family of parallelizable 4-manifolds without complex structure. The twistor space associated with those manifolds admits a complex structure. This is our first class of 6-manifolds with a non standard complex structure. A second class is also build in this work. Finally, and independently, we briefly study the various rational connectedness properties of twistor spaces.
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Contributor : Hal System <>
Submitted on : Tuesday, November 22, 2005 - 4:06:54 PM
Last modification on : Thursday, January 7, 2021 - 4:29:10 PM
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  • HAL Id : tel-00011091, version 1



Guillaume Deschamps. Espaces twistoriels et structures complexes exotiques. Mathématiques [math]. Université Rennes 1, 2005. Français. ⟨tel-00011091⟩



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