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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Killing vector fields and holonomy algebras

Author: Carlos Currás-Bosch
Journal: Proc. Amer. Math. Soc. 90 (1984), 97-102
MSC: Primary 53C20
MathSciNet review: 722424
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Abstract: 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.

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PII: S 0002-9939(1984)0722424-6
Keywords: Complete Riemannian manifolds, Killing vector fields, holonomy algebras
Article copyright: © Copyright 1984 American Mathematical Society