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Mat. Tr., 2013, Volume 16, Number 1, Pages 141–149 (Mi mt253)  

Killing vector fields and the curvature tensor of a Riemannian manifold

Yu. G. Nikonorov

South Mathematical Institute of VSC RAS, Vladikavkaz, Russia

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.

Key words: Riemannian manifold, Killing vector field, homogeneous Riemannian space, curvature tensor, sectional curvature.

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English version:
Siberian Advances in Mathematics, 2014, 24:3, 187–192

Bibliographic databases:

Document Type: Article
UDC: 514.76
Received: 05.05.2012

Citation: Yu. G. Nikonorov, “Killing vector fields and the curvature tensor of a Riemannian manifold”, Mat. Tr., 16:1 (2013), 141–149; Siberian Adv. Math., 24:3 (2014), 187–192

Citation in format AMSBIB
\Bibitem{Nik13}
\by Yu.~G.~Nikonorov
\paper Killing vector fields and the curvature tensor of a~Riemannian manifold
\jour Mat. Tr.
\yr 2013
\vol 16
\issue 1
\pages 141--149
\mathnet{http://mi.mathnet.ru/mt253}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3156677}
\transl
\jour Siberian Adv. Math.
\yr 2014
\vol 24
\issue 3
\pages 187--192
\crossref{https://doi.org/10.3103/S1055134414030055}


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