Branson's Q-curvature in Riemannian and Spin Geometry

Details Branson's Q-curvature in Riemannian and Spin Geometry Branson's Q-curvature in Riemannian and Spin Geometry

2007-09-04

arxiv.org/abs/0709.0345v3

Symmetry, Integrability and Geometry: Methods and Applications 3, 119 (2007) 11 pages

Mathematics

Differential Geometry

14 pages, Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson

Scientific paper

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.

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