Killing Vector Fields of Constant Length on Riemannian Normal Homogeneous Spaces

TL;DR

This paper investigates Killing vector fields of constant length on Riemannian normal homogeneous spaces, expanding understanding beyond symmetric spaces and group manifolds to a broader class of homogeneous spaces.

Contribution

It extends the study of constant length Killing vector fields from symmetric spaces and group manifolds to Riemannian normal homogeneous spaces.

Findings

Identifies conditions for Killing vector fields of constant length in new classes of homogeneous spaces

Provides classification results for such vector fields in Riemannian normal homogeneous spaces

Enhances understanding of isometries with constant displacement in broader geometric contexts

Abstract

Killing vector fields of constant length correspond to isometries of constant displacement. Those in turn have been used to study homogeneity of Riemannian and Finsler quotient manifolds. Almost all of that work has been done for group manifolds or, more generally, for symmetric spaces. This paper extends the scope of research on constant length Killing vector fields to a class of Riemannian normal homogeneous spaces.