Universal curvature identities II

Abstract

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.

15 pages

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Cited by in corpus (7)

• A remark on the invariant theory of real Lie groups
• On second-order, divergence-free tensors
• Dimensional curvature identities on pseudo-Riemannian geometry
• Euler-Lagrange formulas for pseudo-Kaehler manifolds
• On the uniqueness of the Gauss-Bonnet-Chern formula (after Gilkey-Park-Sekigawa)
• Universal curvature identities and Euler Lagrange Formulas for Kaehler manifolds
• A curvature identity on a 6-dimensional Riemannian Manifold and its applications