On the decomposition of global conformal invariants I

Details On the decomposition of global conformal invariants I On the decomposition of global conformal invariants I

2005-09-23

arxiv.org/abs/math/0509571v3

Mathematics

Differential Geometry

65 pages, final version, to appear in Annals of Mathematics

Scientific paper

This is the first of two papers where we address and partially confirm a conjecture of Deser and Schwimmer, originally postulated in high energy physics. The objects of study are scalar Riemannian quantities constructed out of the curvature and its covariant derivatives, whose integrals over compact manifolds are invariant under conformal changes of the underlying metric. Our main conclusion is that each such quantity that locally depends only on the curvature tensor (without covariant derivatives) can be written as a linear combination of the Chern-Gauss-Bonnet integrand and a scalar conformal invariant.

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