Universal curvature identities III
  We examine universal curvature identities for pseudo-Riemannian manifolds with boundary. We determine the Euler-Lagrange equations associated to the Chern-Gauss-Bonnet formula and show that they are given solely in terms of curvature {and the second fundamental form and do not involve covariant derivatives thus generalizing a conjecture of Berger to this context. 
P. Gilkey, J.H. Park, and K. Sekigawa
math.DG