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Feldname	Details
Dewey Class	516.36 (DDC 23)
Titel	Families of Conformally Covariant Differential Operators, Q-Curvature and Holography ([Ebook]) / by Andreas Juhl.
Verfasser	Juhl, Andreas
Other name(s)	SpringerLink (Online service)
Veröffentl	Basel : Birkhäuser , 2009.
Physical Details	XIII, 488 pages : online resource.
Reihe	Progress in mathematics ; 275
ISBN	9783764399009
Summary Note	The central object of the book is a subtle scalar Riemannian curvature quantity in even dimensions which is called Bransonâs Q-curvature. It was introduced by Thomas Branson about 15 years ago in connection with an attempt to systematise the structure of conformal anomalies of determinants of conformally covariant differential operators on Riemannian manifolds. Since then, numerous relations of Q-curvature to other subjects have been discovered, and the comprehension of its geometric significance in four dimensions was substantially enhanced through the studies of higher analogues of the Yamabe problem. The book attempts to reveal some of the structural properties of Q-curvature in general dimensions. This is achieved by the development of a new framework for such studies. One of the main properties of Q-curvature is that its transformation law under conformal changes of the metric is governed by a remarkable linear differential operator: a conformally covariant higher order generalization of the conformal Laplacian. In the new approach, these operators and the associated Q-curvatures are regarded as derived quantities of certain conformally covariant families of differential operators which are naturally associated to hypersurfaces in Riemannian manifolds. This method is at the cutting edge of several central developments in conformal differential geometry in the last two decades such as Fefferman-Graham ambient metrics, spectral theory on PoincarÃ©-Einstein spaces, tractor calculus, and Cartan geometry. In addition, the present theory is strongly inspired by the realization of the idea of holography in the AdS/CFT-duality. This motivates the term holographic descriptions of Q-curvature.:
Contents note	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. Conformally Covariant Families -- Bibliography -- Index.
System details note	Online access to digital resource is restricted to subscription institutions through IP address (only for SISSA users)
Internet Site	http://dx.doi.org/10.1007/978-3-7643-9900-9
LINKS ZU 'VERWANDTEN WERKEN	Schlagwörter: . Differential Geometry . Global analysis . Global Analysis and Analysis on Manifolds . Global differential geometry . Mathematical Methods in Physics . Mathematical Physics . Mathematics . Topological groups . Topological groups, Lie groups . Authors: Juhl, Andreas . Corporate Authors: SpringerLink (Online service) . Series: Progress in mathematics . Classification: 516.36 (DDC 23) .

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Families of Conformally Covariant Differential Operators, Q-Curvature and Holography

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