Communications in Mathematical Physics

, Volume 29, Issue 1, pp 55–59

Conditions on a connection to be a metric connection

  • B. G. Schmidt


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

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • B. G. Schmidt
    • 1
  1. 1.I. Institut für Theoretische PhysikUniversität HamburgGermany

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