Killing vector fields of constant length on compact homogeneous Riemannian manifolds

TL;DR

This paper investigates the structure of Lie algebras associated with the isometry groups of compact homogeneous Riemannian manifolds that admit nontrivial Killing vector fields of constant length.

Contribution

It provides new structural insights into the Lie algebras of isometry groups for these manifolds, expanding understanding of their geometric and algebraic properties.

Findings

Structural results on Lie algebras of isometry groups

Characterization of Killing vector fields of constant length

Implications for the geometry of compact homogeneous manifolds

Abstract

In this paper we present some structural results on the Lie algebras of transitive isometry groups of a general compact homogenous Riemannian manifold with nontrivial Killing vector fields of constant length.