## 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.## References

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## Additional Information

- © Copyright 1984 American Mathematical Society
- 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