Geodesic
Killing vector fields and the curvature tensor of a~Riemannian manifold
Matematičeskie trudy, Tome 16 (2013) no. 1, pp. 141-149

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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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     author = {Yu. G. Nikonorov},
     title = {Killing vector fields and the curvature tensor of {a~Riemannian} manifold},
     journal = {Matemati\v{c}eskie trudy},
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Yu. G. Nikonorov. Killing vector fields and the curvature tensor of a~Riemannian manifold. Matematičeskie trudy, Tome 16 (2013) no. 1, pp. 141-149. http://geodesic.mathdoc.fr/item/MT_2013_16_1_a7/