Chern's conjecture for special affine manifolds

• 成果类型: Article
• 署名作者: Klingler, Bruno
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2017.186.1.2
• 发表日期: 2017
• 页码: 69-95
• 关键词: flat manifolds; geometry; product; bundles; zero

摘要

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.