The deformation of flat connections and affine manifolds |
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Authors: | Mihail Cocos |
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Institution: | 1.Weber State University,Ogden,USA |
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Abstract: | Geodesically complete affine manifolds are quotients of the Euclidean space through a properly discontinuous action of a subgroup
of affine Euclidean transformations. An equivalent definition is that the tangent bundle of such a manifold admits a flat,
symmetric and complete connection. If the completeness assumption is dropped, the manifold is not necessarily obtained as
the quotient of the Euclidean space through a properly discontinuous group of affine transformations. In fact the universal
cover may no longer be the Euclidean space. The main result of this paper states that if a flat connection of a bundle can
be properly deformed into a metric connection then its Euler class vanishes. This is a partial result toward an old question
of Chern. |
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Keywords: | |
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