Title: Complex analytic geometry of complex parallelizable manifolds
Abstract:We investigate complex parallelizable manifolds, i.e., complex manifolds arising as quotients of complex Lie groups by discrete subgroups.Special emphasis is put on quotients by discrete subgroups whi...We investigate complex parallelizable manifolds, i.e., complex manifolds arising as quotients of complex Lie groups by discrete subgroups.Special emphasis is put on quotients by discrete subgroups which are cocompact or at least of finite covolume.These quotient manifolds are studied from a complex-analytic point of view.Topics considered include submanifolds, vector bundles, cohomology, deformations, maps and functions.Furthermore arithmeticity results for compact complex nilmanifolds are deduced.An exposition of basic results on lattices in complex Lie groups is also included, in order to improve accessibility. Resume (Geometric analytique complexe et varietes complexes parallelisables)On etudie les varietes complexes parallelisables, c'est-a-dire les varietes quotients des groupes de Lie complexes par des sous-groupes discrets.On s'mteresse tout particulierement aux quotients par des sous-groupes discrets cocompacts ou de covolume fini.Ces varietes quotients sont etudiees du point de vue de la geometric analytique complexe.On traite notamment les sujets suivants : les sous-varietes, les fibres vectoriels, la cohomologie, les deformations, les applications et les fonctions.De plus, on en deduit des resultats d'arithmeticite pour des nil-varietes complexes compactes.Pour faciliter la lecture du texte, on a inclus un expose de resultats de base sur les reseaux dans les groupes de Lie complexes.Read More