Journal of Differential Geometry

Clifford-Wolf homogeneous Riemannian manifolds

Valerii N. Berestovskii and Yurii G. Nikonorov

Full-text: Open access

Abstract

In this paper, using connections between Clifford-Wolf isometries and Killing vector fields of constant length on a given Riemannian manifold, we classify simply connected Clifford-Wolf homogeneous Riemannian manifolds. We also get the classification of complete simply connected Riemannian manifolds with the Killing property defined and studied previously by J. E. D’Atri and H. K. Nickerson. In the last part of the paper we study properties of Clifford-Killing spaces, that is, real vector spaces of Killing vector fields of constant length, on odd-dimensional round spheres, and discuss numerous connections between these spaces and various classical objects.

Article information

Source
J. Differential Geom. Volume 82, Number 3 (2009), 467-500.

Dates
First available in Project Euclid: 24 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1251122544

Digital Object Identifier
doi:10.4310/jdg/1251122544

Mathematical Reviews number (MathSciNet)
MR2494239

Zentralblatt MATH identifier
1179.53043

Citation

Berestovskii, Valerii N.; Nikonorov, Yurii G. Clifford-Wolf homogeneous Riemannian manifolds. J. Differential Geom. 82 (2009), no. 3, 467--500. doi:10.4310/jdg/1251122544. https://projecteuclid.org/euclid.jdg/1251122544


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