Siberian Mathematical Journal

, Volume 49, Issue 3, pp 395–407 | Cite as

Killing vector fields of constant length on Riemannian manifolds

  • V. N. Berestovskii
  • Yu. G. Nikonorov


We study the nontrivial Killing vector fields of constant length and the corresponding flows on complete smooth Riemannian manifolds. Various examples are constructed of the Killing vector fields of constant length generated by the isometric effective almost free but not free actions of S 1 on the Riemannian manifolds close in some sense to symmetric spaces. The latter manifolds include “almost round” odd-dimensional spheres and unit vector bundles over Riemannian manifolds. We obtain some curvature constraints on the Riemannian manifolds admitting nontrivial Killing fields of constant length.


Riemannian manifold Killing vector field geodesic Sasaki metric 


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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Omsk Branch of the Sobolev Institute of MathematicsOmskRussia
  2. 2.Rubtsovsk Industrial Institute of Altai State Technical UniversityRubtsovskRussia

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