LRGEOM · Low dimensional Riemannian and Lorentzian geometry of constant curvature

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Project objective

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."

Original text from CORDIS.

Participants

• UNIVERSITÉ PAUL SABATIER · TOULOUSECoordinatorFrance

Links

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