The decomposition of global conformal invariants IV: A proposition on local Riemannian invariants

Details The decomposition of global conformal invariants IV: A proposition on local Riemannian invariants The decomposition of global conformal invariants IV: A proposition on local Riemannian invariants

2009-12-18

arxiv.org/abs/0912.3761v1

Mathematics

Differential Geometry

Scientific paper

This is the fourth in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global conformal invariants''; these are defined to be conformally invariant integrals of geometric scalars. The conjecture asserts that the integrand of any such integral can be expressed as a linear combination of a local conformal invariant, a divergence and of the Chern-Gauss-Bonnet integrand. The present paper lays out the second half of this entire work: The second half proves certain purely algebraic statements regarding local Riemannian invariants; these were used extensively in [3,4]. These results may be of independent interest, applicable to related problems.

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