2007/10/08 by Wolfgang Bertram, Bertram, Wolfgang, Manon Didry +1
Mathematics · #17A01 #17B10 #53C15 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:17A01 #msc:17B10 #msc:53C15
paper · pdf · doi:10.48550/arxiv.0710.1543
22 pages, v2: minor corrections
openalex publication_date 2007/10/08 · arxiv created 2009/01/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define symmetric bundles as vector bundles in the category of symmetric spaces; it is shown that this notion is the geometric analog of the one of a representation of a Lie triple system. We show that such a bundle has an underlying reflection space, and we investigate the corresponding forgetful functor both from the point of view of differential geometry and from the point of view of representation theory. This functor is not injective, as is seen by constructing "unusual" symmetric bundle structures on the tangent bundles of certain symmetric spaces.