Local and infinitesimal rigidity of simply connected negatively curved manifolds
Annales de l'Institut Fourier, Volume 66 (2016) no. 6, p. 2507-2523
Let (X,g 0 ) be a simply connected Riemannian manifold with sectional curvature K-1. For a metric g on X which is equal to g 0 outside a compact the identity map of X induces a conformal map id ^ g 0 ,g : g 0 X g X between the boundaries at infinity of X with respect to g 0 and g. We define a function S(g) on the space of geodesics of (X,g 0 ), called the integrated Schwarzian of g, which measures the deviation of this conformal map from being Moebius. We use the integrated Schwarzian to prove local and infinitesimal rigidity results for such metric deformations.
Soit (X,g 0 ) un variété Riemannienne simplement connexe à courbure K-1. Pour une métrique g qui est égale à g 0 en dehors d’un compact l’identité de X s’étend à une application conforme id ^ g 0 ,g : g 0 X g X entre les bords à l’infini de X par rapport à g 0 et g. On définit une fonction S(g) sur l’espace des geodésiques de (X,g 0 ), appelé le Schwarzian integré de g, qui quantifie la déviation de cette application d’être Moebius. On utilise le Schwarzian integré pour démontrer des théorèmes de rigidité locale et infinitesimale pour tels déformations métriques.
Received : 2016-01-11
Accepted : 2016-03-24
Published online : 2016-10-04
DOI : https://doi.org/10.5802/aif.3070
Classification:  53C24
Keywords: Negatively curved manifolds, Moebius, cross-ratio
@article{AIF_2016__66_6_2507_0,
     author = {Biswas, Kingshook},
     title = {Local and infinitesimal rigidity of simply connected negatively curved manifolds},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {66},
     number = {6},
     year = {2016},
     pages = {2507-2523},
     doi = {10.5802/aif.3070},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2016__66_6_2507_0}
}
Local and infinitesimal rigidity of simply connected negatively curved manifolds. Annales de l'Institut Fourier, Volume 66 (2016) no. 6, pp. 2507-2523. doi : 10.5802/aif.3070. https://aif.centre-mersenne.org/item/AIF_2016__66_6_2507_0/

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