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Parallel connections over symmetric spaces

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Abstract

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.

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Authors and Affiliations

  1. University of Pennsylvania, 19104, Philadelphia, PA

    Luis Guijarro

  2. Universidad Autonoma de Madrid, Spain

    Luis Guijarro

  3. University of Texas, 78712, Austin, TX

    Lorenzo Sadun

  4. University of Oklahoma, 73019, Norman, OK

    Gerard Walschap

Authors
  1. Luis Guijarro
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  2. Lorenzo Sadun
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  3. Gerard Walschap
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Corresponding author

Correspondence to Luis Guijarro.

Additional information

Communicated by Karsten Grove

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Guijarro, L., Sadun, L. & Walschap, G. Parallel connections over symmetric spaces. J Geom Anal 11, 265–281 (2001). https://doi.org/10.1007/BF02921966

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  • DOI: https://doi.org/10.1007/BF02921966

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