Hiroshima Mathematical Journal

Geodesic orbit manifolds and Killing fields of constant length

Yuriĭ G. Nikonorov

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The goal of this paper is to clarify connections between Killing fields of constant length on a Rimannian geodesic orbit manifold $(M,g)$ and the structure of its full isometry group. The Lie algebra of the full isometry group of $(M,g)$ is identified with the Lie algebra of Killing fields $\mathfrak{g}$ on $(M,g)$. We prove the following result: If $\mathfrak{a}$ is an abelian ideal of $\mathfrak{g}$, then every Killing field $X\in \mathfrak{a}$ has constant length. On the ground of this assertion we give a new proof of one result of C. Gordon: Every Riemannian geodesic orbit manifold of nonpositive Ricci curvature is a symmetric space.

Article information

Hiroshima Math. J., Volume 43, Number 1 (2013), 129-137.

First available in Project Euclid: 10 May 2013

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Zentralblatt MATH identifier

Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]
Secondary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C35: Symmetric spaces [See also 32M15, 57T15]

Killing fields of constant length homogeneous Riemannian manifolds geodesic orbit spaces symmetric spaces Ricci curvature


Nikonorov, Yuriĭ G. Geodesic orbit manifolds and Killing fields of constant length. Hiroshima Math. J. 43 (2013), no. 1, 129--137. doi:10.32917/hmj/1368217953. https://projecteuclid.org/euclid.hmj/1368217953

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