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Killing vector fields of constant length on Riemannian manifolds

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Abstract

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.

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Authors and Affiliations

  1. Omsk Branch of the Sobolev Institute of Mathematics, Omsk, Russia

    V. N. Berestovskii

  2. Rubtsovsk Industrial Institute of Altai State Technical University, Rubtsovsk, Russia

    Yu. G. Nikonorov

Authors
  1. V. N. Berestovskii
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  2. Yu. G. Nikonorov
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Corresponding author

Correspondence to V. N. Berestovskii.

Additional information

Original Russian Text Copyright © 2008 Berestovskiĭ V. N. and Nikonorov Yu. G.

The first author was supported by the Russian Foundation for Basic Research (Grants 04-01-00315-a, 05-01-00057-a, and 05-01-03016-b). The second author was supported by the Russian Foundation for Basic Research (Grant 05-01-00611-a) and the State Maintenance Program for the Young Science Doctors and Leading Scientific Schools (a Grant of the President of the Russian Federation; Grants NSh-8526.2006.1 and MD-5179.2006.1).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 3, pp. 497–514, May–June, 2008.

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Berestovskii, V.N., Nikonorov, Y.G. Killing vector fields of constant length on Riemannian manifolds. Sib Math J 49, 395–407 (2008). https://doi.org/10.1007/s11202-008-0039-3

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  • DOI: https://doi.org/10.1007/s11202-008-0039-3

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