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Natural connections on the bundle of Riemannian metrics

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Abstract.

Let \(FM,{\cal M}_M\) be the bundles of linear frames and Riemannian metrics of a manifold M, respectively. The existence of a unique Diff M-invariant connection form on \(J^1{\cal M}_M\times _M FM\rightarrow J^1{\cal M}_M\), which is Riemannian with respect to the universal metric on \(J^1{\cal M}_M\times _M TM\), is proved. Applications to the construction of universal Pontryagin and Euler forms, are given.

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Authors and Affiliations

  1. Universidad Complutense Madrid, Madrid, Spain

    R. Ferreiro Pérez

  2. CSIC, Madrid, Spain

    J. Muñoz Masqué

Authors
  1. R. Ferreiro Pérez
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  2. J. Muñoz Masqué
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Authors’ addresses: R. Ferreiro Pérez, Departamento de Economía Financiera y Contabilidad I, UCM, Campus de Somosaguas, 28223 Madrid, Spain; J. Muñoz Masqué, Insituto de Física Aplicada, CSIC, C/Serrano 144, 28006 Madrid, Spain

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Ferreiro Pérez, R., Muñoz Masqué, J. Natural connections on the bundle of Riemannian metrics. Monatsh Math 155, 67–78 (2008). https://doi.org/10.1007/s00605-008-0565-x

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