Q-Curvature, Spectral Invariants, and Representation Theory
Abstract
We give an introductory account of functional determinants of elliptic operators on manifolds and Polyakov-type formulas for their infinitesimal and finite conformal variations. We relate this to extremal problems and to the Q-curvature on even-dimensional conformal manifolds. The exposition is self-contained, in the sense of giving references sufficient to allow the reader to work through all details.
- Publication:
-
SIGMA
- Pub Date:
- September 2007
- DOI:
- 10.3842/SIGMA.2007.090
- arXiv:
- arXiv:0709.2471
- Bibcode:
- 2007SIGMA...3..090B
- Keywords:
-
- conformal differential geometry;
- functional determinant;
- conformal index;
- Mathematics - Differential Geometry;
- Mathematical Physics
- E-Print:
- This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/