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1984

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/7622

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.

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http://doi.org/10.1090/S0002-9939-1984-0722424-6

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Camps vectorials, Àlgebra

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Vector fields, Algebra

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Articles publicats en revistes (Matemàtiques i Informàtica)

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CURRÁS BOSCH, Carlos. Killing vector fields and holonomy algebras. Proceedings of the American Mathematical Society. 1984. Vol. 90, num. 1, pags. 97-102. ISSN 1088-6826. [consulted: 13 of October of 2026]. Available at: https://hdl.handle.net/2445/7622

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