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On Infinitesimal Holonomy and Isotropy Groups
Published online by Cambridge University Press: 22 January 2016
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We have proved in [2] that if the restricted homogeneous holonomy group of a complete Riemannian manifold is contained in the linear isotropy group at every point, then the Riemannian manifold is locally symmetric, that is, the covariant derivatives of the curvature tensor field are zero. The proof of this theorem, however, depended on an insufficiently stated proposition (Theorem 1, [2]). In the present note, we shall give a proof of a more general theorem of the same type.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1957
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