Fibres affines

Details Fibres affines Fibres affines

2001-05-22

arxiv.org/abs/math/0105179v1

Mathematics

Differential Geometry

26 pages, To be published in the Michigan Mathematical Journal

Scientific paper

We study affine maps between affine manifolds. Even when the fibers are compact and diffeomorphic, two of them can inherit different affine structures from the source space. This leads to a fixed linear holonomy deformation theory of the affine structure of an affine manifold. We found various conditions which make the fibers to be affinely isomorphic. We also classify affine bundles which total space is a compact and complete affine manifold.

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