1997/12/22 by Luis Guijarro, Lorenzo Sadun, Guijarro, Luis +3
Mathematics · Medicine · Physics and Astronomy · #53C05 (Primary) #53C07 #53C20 #53C35 (Secondary) #Advanced Differential Geometry Research #Advanced Neuroimaging Techniques and Applications #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #dg-ga #math.DG #msc:53C05 #msc:53C07 #msc:53C20 #msc:53C35
paper · pdf · doi:10.48550/arxiv.dg-ga/9712014
AmS-TeX, 18 pages
arxiv created 1997/12/22 · openalex publication_date 1997/12/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be a simply connected Riemannian symmetric space, with at most one flat direction. We show that every Riemannian (or unitary) vector bundle with parallel curvature over M is an associated vector bundle of a canonical principal bundle, with the connection inherited from the principal bundle. The problem of finding Riemannian (or unitary) vector bundles with parallel curvature then reduces to finding representations of the structure group of the canonical principal bundle.