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Article Dans Une Revue European Journal of Mathematics Année : 2020

GENERALIZED HOLOMORPHIC CARTAN GEOMETRIES

Résumé

This is largely a survey paper, dealing with Cartan geometries in the complex analytic category. We first remind some standard facts going back to the seminal works of F. Klein, E. Cartan and C. Ehresmann. Then we present the concept of a branched holomorphic Cartan geometry which was introduced by the authors in [BD]. It generalizes to higher dimension the notion of a branched (flat) complex projective structure on a Riemann surface introduced by Mandelbaum. This new framework is much more flexible than that of the usual holomorphic Cartan geometries (e.g. all compact complex projective manifolds admit branched holomorphic projective structures). At the same time, this new definition is rigid enough to enable us to classify branched holomorphic Cartan geometries on compact simply connected Calabi-Yau manifolds.
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Dates et versions

hal-01871795 , version 1 (11-09-2018)

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  • HAL Id : hal-01871795 , version 1

Citer

Indranil Biswas, Sorin Dumitrescu. GENERALIZED HOLOMORPHIC CARTAN GEOMETRIES. European Journal of Mathematics, 2020, Special issue dedicated to the memory of Stefan Papadima, 6 (3), pp.661-680. ⟨hal-01871795⟩
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