Geodesic
Chern’s conjecture for special affine manifolds
Bruno Klingler1
1 Institut de Mathématiques de Jussieu, Paris, France and Institut Universitaire de France, Paris, France
Annals of mathematics, Tome 186 (2017) no. 1, pp. 69-95.

Voir la notice de l'article provenant de la source Annals of Mathematics website

An affine manifold $X$ in the sense of differential geometry is a differentiable manifold admitting an atlas of charts with value in an affine space, with locally constant affine change of coordinates. Equivalently, it is a manifold whose tangent bundle admits a flat torsion free connection. Around 1955 Chern conjectured that the Euler characteristic of any compact affine manifold has to vanish. In this paper we prove Chern’s conjecture in the case where $X$ moreover admits a parallel volume form.
DOI : 10.4007/annals.2017.186.1.2

Bruno Klingler 1

1 Institut de Mathématiques de Jussieu, Paris, France and Institut Universitaire de France, Paris, France 
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Bruno Klingler. Chern’s conjecture for special affine manifolds. Annals of mathematics, Tome 186 (2017) no. 1, pp. 69-95. doi : 10.4007/annals.2017.186.1.2. http://geodesic.mathdoc.fr/articles/10.4007/annals.2017.186.1.2/

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