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Parallel Connections Over Symmetric Spaces

Luis Guijarro·Lorenzo Sadun·Gerard Walschap
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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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BibTeXRIS

Luis Guijarro, Lorenzo Sadun, Gerard Walschap. 1997-12-22. Parallel Connections Over Symmetric Spaces. https://arxiv.org/abs/dg-ga/9712014

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