Parallel Connections Over Symmetric Spaces
dg-ga
2007-05-23 v1 Differential Geometry
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.
Cite
@article{arxiv.dg-ga/9712014,
title = {Parallel Connections Over Symmetric Spaces},
author = {Luis Guijarro and Lorenzo Sadun and Gerard Walschap},
journal= {arXiv preprint arXiv:dg-ga/9712014},
year = {2007}
}
Comments
AmS-TeX, 18 pages