  We show that any universal curvature identity which holds in the Riemannian
setting extends naturally to the pseudo-Riemannian setting. Thus the
Euh-Park-Sekigawa identity also holds for pseudo-Riemannian manifolds. We study
the Euler-Lagrange equations associated to the Chern-Gauss-Bonnet formula and
show that as in the Riemannian setting, they are given solely in terms of
curvature (and not in terms of covariant derivatives of curvature) even in the
pseudo-Riemannian setting.
