Home » Families Of Conformally Covariant Differential Operators, Q Curvature And Holography by Andreas Juhl
Families Of Conformally Covariant Differential Operators, Q Curvature And Holography Andreas Juhl

Families Of Conformally Covariant Differential Operators, Q Curvature And Holography

Andreas Juhl

Published May 13th 2009
ISBN : 9783764398996
Hardcover
488 pages
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 About the Book 

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 covariantMoreThe 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 central developments in conformal differential geometry in the last two decades (Fefferman-Graham ambient metrics, spectral theory on Poincare-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.