黎曼Holonomy与Algebraic Geometry
Riemannian Holonomy and Algebraic Geometry
摘要：
这篇综述论文致力于研究具有特殊完整性的黎曼流形。任何n维的黎曼流形都有一个SO（n）的闭子群，即和乐群;这是度量的最基本不变式之一。一个著名的定理伯杰给出了一个完整的（而不是小）名单的团体可以出现。令人惊讶的是，完整性小于SO（n）的紧致流形都与代数几何有某种联系。这导致研究特殊的代数簇（卡-丘，复辛或复接触流形），其中黎曼几何提出了有趣的问题。
英文摘要：
This survey paper is devoted to Riemannian manifolds with special holonomy. To any Riemannian manifold of dimension n is associated a closed subgroup of SO(n), the holonomy group; this is one of the most basic invariants of the metric. A famous theorem of Berger gives a complete (and rather small) list of the groups which can appear. Surprisingly, the compact manifolds with holonomy smaller than SO(n) are all related in some way to Algebraic Geometry. This leads to the study of special algebraic varieties (Calabi-Yau, complex symplectic or complex contact manifolds) for which Riemannian geometry rises interesting questions.
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