Nearly Kähler geometry

近Kähler流形和几乎Kähler流形构成了一类重要的几乎厄米特流形。他们被研究了很多年。然而，近Kähler流形在弦理论中的应用在最近几年重新引起了人们的兴趣。该项目的目的是研究近Kähler流形和几乎Kähler流形，它应该接近于6维近Kähler流形的分类和附加曲率条件下的几乎Kähler流形的分类。对这两个几何的研究统一于对正则厄米特联络及其性质的考虑。

Nearly and almost Kähler manifolds form important classes of almost Hermitian manifolds. They were studied for many years. However, an application of nearly Kähler manifolds in string theory led to a renewed interest in recent years. Aim of the proposed project is a study of nearly and almost Kähler manifolds, which should approach a classification of nearly Kähler manifolds in dimension 6 and a classification of almost Kähler manifolds under additional curvature conditions. The study of these two geometries is unified by the consideration of the canonical Hermitian connection and its properties.