%0 Journal Article
%T Two Kazdan-Warner type identities for the renormalized volume coefficients and the Gauss-Bonnet curvatures of a Riemannian metric
%A Bin Guo
%A Zheng-Chao Han
%A Haizhong Li
%J Mathematics
%D 2009
%I arXiv
%X In this note, we prove two Kazdan-Warner type identities involving $v^{(2k)}$, the renormalized volume coefficients of a Riemannian manifold $(M^n,g)$, and $G_{2r}$, the so-called Gauss-Bonnet curvature, and a conformal Killing vector field on $(M^n,g)$. In the case when the Riemannian manifold is locally conformally flat, $v^{(2k)}=(-2)^{-k}\sigma_k$, $G_{2r}(g)=\frac{4^r(n-r)!r!}{(n-2r)!}\sigma_r$, and our results reduce to earlier ones established by Viaclovsky and by the second author.
%U http://arxiv.org/abs/0911.4649v1