Clifford-Wolf homogeneous Riemannian manifolds

Details Clifford-Wolf homogeneous Riemannian manifolds Clifford-Wolf homogeneous Riemannian manifolds

2008-03-31

arxiv.org/abs/0803.4368v1

Mathematics

Differential Geometry

24 pages

Scientific paper

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.

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