Universal curvature identities II

  • Gilkey P
  • Park J
  • Sekigawa K
  • 3


    Mendeley users who have this article in their library.
  • 9


    Citations of this article.


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.

Author-supplied keywords

  • Chern-Gauss-Bonnet theorem
  • Euh-Park-Sekigawa identity
  • Euler-Lagrange equations
  • Pfaffian

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document


  • P. Gilkey

  • J. H. Park

  • K. Sekigawa

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free