Nearly Kähler geometry

近似和近似Kähler流形构成了一类重要的近似厄米流形。他们被研究了很多年。然而，近年来，近Kähler流形在弦理论中的应用重新引起了人们的兴趣。本课题的目的是研究近似和近似Kähler流形，接近6维近似Kähler流形的分类和附加曲率条件下近似Kähler流形的分类。这两种几何的研究是统一的考虑标准厄米连接及其性质。

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.