A curvature identity on a 6-dimensional Riemannian Manifold and its   applications
  We derive a curvature identity that holds on any 6-dimensional Riemannian manifold, from the Chern-Gauss-Bonnet theorem for a 6-dimensional closed Riemannian manifold. We also introduce some applications of this curvature identity. 
Yunhee Euh, JeongHyeong Park and Kouei Sekigawa
math.DG