rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Families of Conformally Covariant Differential Operators, Q-Curvature and Holography
  name:
    name part: Juhl, Andreas.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: sz
    date issued: 2009
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIII, 490 p. online resource.
  abstract: The central object of the book is a subtle scalar Riemannian curvature quantity in even dimensions which is called Branson’s 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 Poincaré-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.
  table of contents: Spaces, Actions, Representations and Curvature -- Conformally Covariant Powers of the Laplacian, Q-curvature and Scattering Theory -- Paneitz Operator and Paneitz Curvature -- Intertwining Families -- Conformally Covariant Families.
  note: by Andreas Juhl.
  subject:
    topic: Mathematics
  subject:
    topic: Topological groups
  subject:
    topic: Lie groups
  subject:
    topic: Global analysis (Mathematics)
  subject:
    topic: Manifolds (Mathematics)
  subject:
    topic: Differential geometry
  subject:
    topic: Physics
  subject:
    topic: Mathematics
  subject:
    topic: Differential Geometry
  subject:
    topic: Topological Groups, Lie Groups
  subject:
    topic: Global Analysis and Analysis on Manifolds
  subject:
    topic: Mathematical Methods in Physics
  classification: QA641-670
  classification: 516.36
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Progress in Mathematics ; 275
  identifier: 9783764399009
  identifier: http://dx.doi.org/10.1007/978-3-7643-9900-9
  record info:
    record creation date: 100301
    record change date: 20151031021042.0
    record identifier: 978-3-7643-9900-9