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In this paper we develop the basic tools for a classification of Killingvector fields of constant length on pseudo--riemannian homogeneous spaces. Thisextends a recent paper of M. Xu and J. A. Wolf, which classified the pairs$(M,\xi)$ where $M = G/H$ is a Riemannian normal homogeneous space, $G$ is acompact simple Lie group, and $\xi \in \mathfrak{g}$ defines a nonzero Killingvector field of constant length on $M$. The method there was directcomputation. Here we make use of the moment map $M \to \mathfrak{g}^*$ and theflag manifold structure of Ad(G)$\xi$ to give a shorter, more geometric proofwhich does not require compactness and which is valid in the pseudo--riemanniansetting. In that context we break the classification problem into three parts.The first is easily settled. The second concerns the cases where $\xi$ iselliptic and $G$ is simple (but not necessarily compact); that case is our mainresult here. The third, which remains open, is a more combinatorial probleminvolving elements of the first two.

Toward a Classification of Killing Vector Fields of Constant Length on Pseudo--Riemannian Normal Homogeneous Spaces