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Mathematics > Differential Geometry

arXiv:0710.1543 (math)
[Submitted on 8 Oct 2007 (v1), last revised 9 Jan 2009 (this version, v2)]

Title:Symmetric bundles and representations of Lie triple systems

Authors:Wolfgang Bertram (IECN), Manon Didry (IECN)
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Abstract: 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.
Comments: 22 pages, v2: minor corrections
Subjects: Differential Geometry (math.DG)
MSC classes: 17A01, 17B10, 53C15
Cite as: arXiv:0710.1543 [math.DG]
  (or arXiv:0710.1543v2 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.0710.1543

Submission history

From: Wolfgang Bertram [view email] [via CCSD proxy]
[v1] Mon, 8 Oct 2007 13:11:33 UTC (40 KB)
[v2] Fri, 9 Jan 2009 13:37:10 UTC (40 KB)
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