  We study scalar and symmetric 2-form valued universal curvature identities.
We use this to establish the Gauss-Bonnet theorem using heat equation methods,
to give a new proof of a result of Kuz'mina and Labbi concerning the
Euler-Lagrange equations of the Gauss-Bonnet integral, and to give a new
derivation of the Euh-Park-Sekigawa identity.
