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March 2013 Geodesic orbit manifolds and Killing fields of constant length
Yuriĭ G. Nikonorov
Hiroshima Math. J. 43(1): 129-137 (March 2013). DOI: 10.32917/hmj/1368217953

Abstract

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.

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Yuriĭ G. Nikonorov. "Geodesic orbit manifolds and Killing fields of constant length." Hiroshima Math. J. 43 (1) 129 - 137, March 2013. https://doi.org/10.32917/hmj/1368217953

Information

Published: March 2013
First available in Project Euclid: 10 May 2013

zbMATH: 1276.53046
MathSciNet: MR3066528
Digital Object Identifier: 10.32917/hmj/1368217953

Subjects:
Primary: 53C20
Secondary: 53C25, 53C35

Rights: Copyright © 2013 Hiroshima University, Mathematics Program

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Vol.43 • No. 1 • March 2013
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