100, rue des maths 38610 Gières / GPS : 45.193055, 5.772076 / Directeur : Thierry Gallay

Christian El Emam

On immersions of surfaces into the space of lines of H^3: a link between complex-valued metrics and projective structures
Thursday, 18 April, 2019 - 14:00
Résumé : 

The study of immersions of a smooth manifold M into holomorphic Riemannian manifolds suggests to define the notion of comple-valued) metrics, namely complex quadratic forms on ℂTM
with some condition of non-degeneracy.

The aim of the talk is to show some geometric properties of complex metrics which can be deduced from the study of this kind of immersions: in particular, we will present a correspondence between complex metrics with constant curvature and some pairs of developing maps for projective structures.

Time permitting, we will show a Uniformization Theorem in this setting and an application to the theory of immersions in ℍ3
.

This is joint work with Francesco Bonsante.

Institution de l'orateur : 
Pavia
Thème de recherche : 
Théorie spectrale et géométrie
Salle : 
4
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