Parallel Connections Over Symmetric Spaces

Details Parallel Connections Over Symmetric Spaces Parallel Connections Over Symmetric Spaces

1997-12-22

arxiv.org/abs/dg-ga/9712014v1

Mathematics

Differential Geometry

AmS-TeX, 18 pages

Scientific paper

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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