The Decomposition of Global Conformal Invariants (AM-182) - Annals of Mathematics Studies 207 (Hardback)
  • The Decomposition of Global Conformal Invariants (AM-182) - Annals of Mathematics Studies 207 (Hardback)
zoom

The Decomposition of Global Conformal Invariants (AM-182) - Annals of Mathematics Studies 207 (Hardback)

(author)
£158.00
Hardback 568 Pages / Published: 18/05/2012
  • We can order this

Usually dispatched within 1 week

  • This item has been added to your basket
This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question concerns conformally invariant functionals on the space of Riemannian metrics over a given manifold. These functionals act on a metric by first constructing a Riemannian scalar out of it, and then integrating this scalar over the manifold. Suppose this integral remains invariant under conformal re-scalings of the underlying metric. What information can one then deduce about the Riemannian scalar? Deser and Schwimmer asserted that the Riemannian scalar must be a linear combination of three obvious candidates, each of which clearly satisfies the required property: a local conformal invariant, a divergence of a Riemannian vector field, and the Chern-Gauss-Bonnet integrand. This book provides a proof of this conjecture. The result itself sheds light on the algebraic structure of conformal anomalies, which appear in many settings in theoretical physics. It also clarifies the geometric significance of the renormalized volume of asymptotically hyperbolic Einstein manifolds. The methods introduced here make an interesting connection between algebraic properties of local invariants--such as the classical Riemannian invariants and the more recently studied conformal invariants--and the study of global invariants, in this case conformally invariant integrals. Key tools used to establish this connection include the Fefferman-Graham ambient metric and the author's super divergence formula.

Publisher: Princeton University Press
ISBN: 9780691153476
Number of pages: 568
Weight: 765 g
Dimensions: 235 x 152 x 28 mm

You may also be interested in...

Trigonometry Workbook For Dummies
Added to basket
Visual Complex Analysis
Added to basket
Introducing Fractals
Added to basket
Platonic and Archimedean Solids
Added to basket
Measurement
Added to basket
£16.95
Paperback
Islamic Design
Added to basket
£5.99
Paperback
Curves and Singularities
Added to basket
Elliptic Tales
Added to basket
£13.99
Paperback
Euclid's Elements
Added to basket
£21.99
Paperback
An Introduction to Manifolds
Added to basket
Maths for Science
Added to basket
£37.99
Paperback
Fractal Geometry
Added to basket
Trigonometry For Dummies
Added to basket
Fractals: A Very Short Introduction
Added to basket

Please sign in to write a review

Your review has been submitted successfully.