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The radiance obstruction and parallel forms on affine manifolds. (English) Zbl 0561.57014

A differentiable manifold M is affine iff M has an atlas with affine coordinate transformations. M is called radiant iff there is an atlas on M with linear coordinate transformations. The obstruction on an affine M for M to be radiant is a one-dimensional cohomology class \(c_ M\) with coefficients in the flat tangent bundle of M. The cohomology class of a parallel exterior k form on the affine M is expressed in terms of the kth exterior power of \(c_ M\). This applies in particular to parallel volume forms. Restrictions are given for the holonomy and topology of compact affine manifolds.
Reviewer: A.Aeppli

MSC:

57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
57R22 Topology of vector bundles and fiber bundles
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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