Killing vector fields of constant length on compact homogeneous Riemannian manifolds

2015/04/30 by Yu. G. Nikonorov · 10 citations
Mathematics · Physics and Astronomy · #Adjoint representation of a Lie algebra #Advanced Differential Geometry Research #Combinatorics #Constant (computer programming) #Differential geometry #Fundamental vector field #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Homogeneous #Isometry (Riemannian geometry) #Isometry group #Killing vector field #Lie algebra #Lie conformal algebra #Lie group #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Pure mathematics #Ricci-flat manifold #Riemannian geometry #Riemannian manifold #Scalar curvature #Vector field #math.DG #msc:53C20 #msc:53C25 #msc:53C30 #msc:53C35

paper · pdf · doi:10.1007/s10455-015-9472-2

published in Annals of Global Analysis and Geometry 48(4), 305-330 (Springer Science+Business Media) · 26 pages, small revision, accepted for publication in Annals of Global Analysis and Geometry

arxiv created 2015/05/28 · openalex publication_date 2015/06/10 · arxiv updated 2020/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Differential Geometry, Lie Groups, and Symmetric Spaces
• Locally symmetric homogeneous spaces
• Clifford-Wolf homogeneous Randers spaces
• Toward a Classification of Killing Vector Fields of Constant Length on Pseudo--Riemannian Normal Homogeneous Spaces
• Einstein Manifolds

Cited by

• Geodesic orbit Riemannian spaces with two isotropy summands. I