Universal curvature identities II
Differential Geometry
2015-06-03 v1
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.
Keywords
Cite
@article{arxiv.1111.1380,
title = {Universal curvature identities II},
author = {Peter B. Gilkey and JeongHyeong Park and Kouei Sekigawa},
journal= {arXiv preprint arXiv:1111.1380},
year = {2015}
}
Comments
15 pages