Beijing Institute of Mathematical Sciences and Applications

The (strict) nearly Kähler manifolds form a special class of almost Hermitian manifolds including the 6-sphere whose almost complex structure is induced by octonionic multiplication. It is characterized by the fact that the metric cone is a G2-manifold, a manifold whose holonomy group is contained in the exceptional Lie group G2. So nearly Kähler manifolds will play a role in the study of singular G2-manifolds.
In this course, I will introduce various topics of nearly Kähler geometry such as relation to spinors or G2 geometry/some basic algebraic properties/deformation theory/classification of homogeneous nearly Kähler manifolds/construction of cohomogeneity one nearly Kähler manifolds.