Communications in Mathematical Physics

, Volume 29, Issue 1, pp 55–59

Conditions on a connection to be a metric connection


  • B. G. Schmidt
    • I. Institut für Theoretische PhysikUniversität Hamburg

DOI: 10.1007/BF01661152

Cite this article as:
Schmidt, B.G. Commun.Math. Phys. (1973) 29: 55. doi:10.1007/BF01661152


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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© Springer-Verlag 1973