Natural connections on the bundle of Riemannian metrics

Details Natural connections on the bundle of Riemannian metrics Natural connections on the bundle of Riemannian metrics

2005-07-04

arxiv.org/abs/math/0507075v1

Mathematics

Differential Geometry

Scientific paper

Let $FM,\mathcal{M}_M$ be the bundles of linear frames and Riemannian metrics of a manifold $M$, respectively. The existence of a unique $\mathrm{Diff}M$-invariant connection form on $J^1\mathcal{M}_M\times_MFM\to J^1\mathcal{M}_M$, which is Riemannian with respect to the universal metric on $J^1\mathcal{M}_M\times_MTM$, is proved. Aplications to the construction of universal Pontryagin and Euler forms, are given.

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