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Siberian Advances in Mathematics

, Volume 24, Issue 3, pp 187–192 | Cite as

Killing vector fields and the curvature tensor of a Riemannian manifold

  • Yu. G. Nikonorov
Article
  • 90 Downloads

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.

Keywords

Riemannian manifold Killing vector field homogeneous Riemannian space curvature tensor sectional curvature 

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Copyright information

© Allerton Press, Inc. 2014

Authors and Affiliations

  1. 1.Southern Mathematical Institute of the Vladikavkaz Scientific Center of RAS and the Government of the Republic of North Ossetia-AlaniaVladikavkazRussia

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