Families of conformally covariant differential operators, Q-curvature and holography

The central object of the book is Q-curvature. This important and subtle scalar Riemannian curvature quantity was introduced by Tom Branson about 15 year ago in connection with variational formulas for determinants of conformally covariant differential operators. The book studies structural properties of Q-curvature from an extrinsic point of view by regarding it as a derived quantity of certain conformally covariant families of differential operators which are associated to hypersurfaces. The new approach is at the cutting edge of centraldevelopments in conformal differential geometry in the last two decades (Fefferman-Graham ambient metrics, spectral theory on Poincaré-Einstein spaces, tractor calculus, Verma modules and Cartan geometry). The theory of conformally covariant families is inspired by the idea of holography in the AdS/CFT-duality. Among other things, it naturally leads to a holographic description of Q-curvature. The methods admit generalizations in various directions. First monograph dealing with Branson’s Q-curvature Develops a new perspective on the subject, presents original results and suggests new research programs Combines ideasof theoretical physics, differential geometry and geometric analysis INDICE: Preface.- 1. Introduction.- 2. Spaces, Actions, Representations and Curvature.- 3. Powers of the Laplacian, Q-Curvature and Scattering.- 4. Paneitz Operator and Paneitz Curvature.- 5. Intertwining Families.- 6. ConformallyCovariant Families.- Bibliography.- Index.

• ISBN: 978-3-7643-9899-6
• Editorial: Birkhaüser
• Encuadernacion: Cartoné
• Páginas: 500
• Fecha Publicación: 01/05/2009
• Nº Volúmenes: 1
• Idioma: Inglés