Killing vector fields and the curvature tensor of a Riemannian manifold |
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| Authors: | Yu. G. Nikonorov |
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| Affiliation: | 1. Southern Mathematical Institute of the Vladikavkaz Scientific Center of RAS and the Government of the Republic of North Ossetia-Alania, Vladikavkaz, 362027, Russia
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| Abstract: | We find a convenient expression for the value of the covariant curvature 4-tensor of an arbitrary Riemannian manifold on a quadruple of its Killing vector fields. With its use, we in particular obtain a simple deduction of the well-known formula to calculate the sectional curvature of a homogeneous Riemannian space. |
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