Geodesic
On the decomposition of global conformal invariants, I
Spyros Alexakis1
1Department of Mathematics<br/>Massachusetts Institute of Technology<br/>77 Massachusetts Avenue<br/>Cambridge, MA 02139-4307<br/>United States
Annals of mathematics, Tome 170 (2009) no. 3, pp. 1241-1306
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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.

DOI : 10.4007/annals.2009.170.1241

Spyros Alexakis  1

1 Department of Mathematics<br/>Massachusetts Institute of Technology<br/>77 Massachusetts Avenue<br/>Cambridge, MA 02139-4307<br/>United States 
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Spyros Alexakis. On the decomposition of global conformal invariants, I. Annals of mathematics, Tome 170 (2009) no. 3, pp. 1241-1306. doi: 10.4007/annals.2009.170.1241

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