Prerequisite

Basics of Riemmanian geometry

Abstract

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.

Lecturer Intro.

Kotaro Kawai got a bachelor's degree and a master's degree from the university of Tokyo, and received his Ph.D from Tohoku university in 2013. He was an assistant professor at Gakushuin university in Japan, then he moved to BIMSA this year. Gakushuin University was established as an educational institution for the imperial family and peers, and even today, some members of the imperial family attend this university. There are many eminent professors and Kunihiko Kodaira worked at this university. He majors in differential geometry, focusing on manifolds with exceptional holonomy. These manifolds are considered to be analogues of Calabi-Yau manifolds, and higher dimensional analogues of gauge theory are expected on these manifolds. This topic is also related to physics, and he think that this is an exciting research field.