The radiance obstruction and parallel forms on affine manifolds

Goldman, William; Hirsch, Morris W.

doi:10.1090/S0002-9947-1984-0760977-7

The radiance obstruction and parallel forms on affine manifolds
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by William Goldman and Morris W. Hirsch PDF

Trans. Amer. Math. Soc. 286 (1984), 629-649 Request permission

Abstract:

A manifold $M$ is affine if it is endowed with a distinguished atlas whose coordinate changes are locally affine. When they are locally linear $M$ is called radiant. The obstruction to radiance is a one-dimensional class ${c_M}$ with coefficients in the flat tangent bundle of $M$. Exterior powers of ${c_M}$ give information on the existence of parallel forms on $M$, especially parallel volume forms. As applications, various kinds of restrictions are found on the holonomy and topology of compact affine manifolds.

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