Natural connections on the bundle of Riemannian metrics

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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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Differential Geometry, Primary 53A55; Secondary 53B05, 53B21, 57R20, 58A20, 58D19

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http://salesiana.dossiersoluciones.com/handle/123456789/75673

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0507075
 http://arxiv.org/abs/math/0507075

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arXiv