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Transactions of the American Mathematical Society

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The radiance obstruction and parallel forms on affine manifolds


Authors: William Goldman and Morris W. Hirsch
Journal: Trans. Amer. Math. Soc. 286 (1984), 629-649
MSC: Primary 57R99; Secondary 53C20, 55R25
DOI: https://doi.org/10.1090/S0002-9947-1984-0760977-7
MathSciNet review: 760977
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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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DOI: https://doi.org/10.1090/S0002-9947-1984-0760977-7
Article copyright: © Copyright 1984 American Mathematical Society

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