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Killing vector fields and holonomy algebras

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We prove that for each Killing vector field $ X$ on a complete Riemannian manifold, whose orthogonal distribution is involutive, the $ (1,1)$ skew-symmetric operator $ {A_X}$ associated to $ X$ by $ {A_X} = {L_X} - {\nabla _X}$ lies in the holonomy algebra at each point. By using the same techniques, we also study when that operator lies in the infinitesimal and local holonomy algebras respectively.

# metadata.dc.relation.isformatof[].value
Reproducció digital del document publicat en format paper, proporcionada per JSTOR http://www.jstor.org/stable/2044677.

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Proceedings of the American Mathematical Society, 1984, vol. 90, núm. 1, p. 97-102.

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Killing vector fields and holonomy algebras