Universal curvature identities III

2012/09/25 by Gilkey, P., Park, J. H., Sekigawa, K.
#53B20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1209.5481

Abstract

We examine universal curvature identities for pseudo-Riemannian manifolds with boundary. We determine the Euler-Lagrange equations associated to the Chern-Gauss-Bonnet formula and show that they are given solely in terms of curvature and the second fundamental form and do not involve covariant derivatives thus generalizing a conjecture of Berger to this context.

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