À propos des deuxième et troisième espaces de cohomologie de l'algèbre de Lie de Poisson d'une variété symplectique
Some aspects of Duistermaat-Heckman formula in finite dimensions are reviewed. We especulate with some of its possible extensions to infinite dimensions. In particular we review the localization principle and the geometry of loop spaces following Witten and Atiyah?s insight.
In this article, we prove new stability results for almost-Einstein hypersurfaces of the Euclidean space, based on previous eigenvalue pinching results. Then, we deduce some comparable results for almost umbilical hypersurfaces.