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Low dimensional Riemannian and Lorentzian geometry of constant curvature

Objectif

The aim of the present project consists in detecting fundamental structures, which allow a unified understanding of low dimensional Riemannian and Lorentzian manifolds of constant curvature.

The point of view is that of Wick rotation-rescaling theory recently outlined by Benedetti and Bonsante. In this framework ends of geometrically finite hyperbolic manifolds support a natural Lorentzian metric for any fixed constant curvature.

The first objective is to investigate the relationships between classical ending invariants and these "ending spacetimes". This should provide a new insight in both hyperbolic geometry and gravity in dimension 3. On the other hand the Wick rotation-rescaling theory should be further extended in order to include the case of ends of an y complete hyperbolic 3-manifolds of finite type.

The present project falls within the timeline research area of 3D-gravity that has involved common efforts of both Mathematicians and Physicists in last years. Actually a deep motivation of the project is t o give a strong geometric support to recent 3D quantum field theories.

Champ scientifique (EuroSciVoc)

Mots‑clés

Thème(s)

Appel à propositions

FP6-2004-MOBILITY-5
Voir d’autres projets de cet appel

Régime de financement

EIF - Marie Curie actions-Intra-European Fellowships

Coordinateur

UNIVERSITE PAUL SABATIER
Contribution de l’UE
Aucune donnée
Coût total
Aucune donnée