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Conditions on a connection to be a metric connection

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Abstract

It is shown that a torsion free linear connection is determined by a metric of given signature if and only if its holonomy group is a subgroup of the orthogonal group corresponding to the signature.

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References

  1. Kobayashi, S., Nomizu, K.: Foundations of differential geometry, Vol. 1. New York: Interscience 1963.

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Authors and Affiliations

  1. I. Institut für Theoretische Physik, Universität Hamburg, Germany

    B. G. Schmidt

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  1. B. G. Schmidt
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Schmidt, B.G. Conditions on a connection to be a metric connection. Commun.Math. Phys. 29, 55–59 (1973). https://doi.org/10.1007/BF01661152

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  • DOI: https://doi.org/10.1007/BF01661152

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