Conditions on a connection to be a metric connection
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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.Kobayashi, S., Nomizu, K.: Foundations of differential geometry, Vol. 1. New York: Interscience 1963.Google Scholar
© Springer-Verlag 1973