Universal curvature identities II

Details Universal curvature identities II Universal curvature identities II

2011-11-06

arxiv.org/abs/1111.1380v1

Mathematics

Differential Geometry

15 pages

Scientific paper

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.

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