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. ...
Read More
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.
Read Less
Add this copy of The Decomposition of Global Conformal Invariants (Am to cart. $36.00, very good condition, Sold by Academybookshop rated 3.0 out of 5 stars, ships from Long Island City, NY, UNITED STATES, published 2012 by Princeton University Press.
Add this copy of The Decomposition of Global Conformal Invariants to cart. $46.61, fair condition, Sold by Devils In The Detail Ltd rated 4.0 out of 5 stars, ships from Oxford, OXFORDSHIRE, UNITED KINGDOM, published 2012 by Princeton University Press.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Fair. Picture Shown is For Illustration Purposes Only, Please See Below For Further Details CONDITION-VERY GOOD light wear and scuff marks to cover, pages in nice condition, shipped from the UK. Trade paperback (US). Glued binding. 464 p. Contains: Illustrations. Annals of Mathematics Studies, 182.
Add this copy of The Decomposition of Global Conformal Invariants (Am to cart. $75.54, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2012 by Princeton University Press.
Add this copy of The Decomposition of Global Conformal Invariants to cart. $86.34, like new condition, Sold by GreatBookPrices rated 4.0 out of 5 stars, ships from Columbia, MD, UNITED STATES, published 2012 by Princeton University Press.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Fine. Trade paperback (US). Glued binding. 464 p. Contains: Illustrations. Annals of Mathematics Studies, 182. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
Add this copy of The Decomposition of Global Conformal Invariants to cart. $86.35, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2012 by Princeton University Press.
Add this copy of The Decomposition of Global Conformal Invariants to cart. $91.30, new condition, Sold by GreatBookPrices rated 4.0 out of 5 stars, ships from Columbia, MD, UNITED STATES, published 2012 by Princeton University Press.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
New. Trade paperback (US). Glued binding. 464 p. Contains: Illustrations. Annals of Mathematics Studies, 182. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
