%0 Journal Article
%T Branson's Q-curvature in Riemannian and Spin Geometry
%A Oussama Hijazi
%A Simon Raulot
%J Mathematics
%D 2007
%I arXiv
%X On a closed 4-dimensional Riemannian manifold, we give a lower bound for the square of the first eigenvalue of the Yamabe operator in terms of the total Branson's Q-curvature. As a consequence, if the manifold is spin, we relate the first eigenvalue of the Dirac operator to the total Branson's Q-curvature. On a closed n-dimensional manifold, $n\ge 5$, we compare the three basic conformally covariant operators : the Branson-Paneitz, the Yamabe and the Dirac operator (if the manifold is spin) through their first eigenvalues. Equality cases are also characterized.
%U http://arxiv.org/abs/0709.0345v3