Conditions on a connection to be a metric connection
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- Schmidt, B.G. Commun.Math. Phys. (1973) 29: 55. doi:10.1007/BF01661152
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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.
© Springer-Verlag 1973