Communications in Mathematical Physics

, Volume 29, Issue 1, pp 55-59

First online:

Conditions on a connection to be a metric connection

  • B. G. SchmidtAffiliated withI. Institut für Theoretische Physik, Universität Hamburg

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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.