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New invariants in CR and contact geometry

Abstract : Cauchy-Riemann geometry, CR for short, is the natural geometry of real pseudoconvex hypersurfaces of C^{n+1} for ngeq 1. We consider the generic case when CR manifolds are contact manifolds. CR geometry presents strong analogies with conformal geometry; hence, known invariants and techniques of conformal geometry can be transported to that context. We focus in this thesis on two such invariants. In a first part, using asymptotically complex hyperbolic geometry, we introduce a CR covariant differential operator on maps from a CR manifold to a Riemannian manifold, which coincides on functions with the CR Paneitz operator. In a second part, we propose a Yamabe invariant for contact manifolds which admit a CR structure, and we study its behaviour under connected sum.
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https://tel.archives-ouvertes.fr/tel-01977216
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  • HAL Id : tel-01977216, version 1

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Gautier Dietrich. New invariants in CR and contact geometry. Differential Geometry [math.DG]. Université Montpellier, 2018. English. ⟨NNT : 2018MONTS016⟩. ⟨tel-01977216⟩

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