The main subject of the course is the geometry of Riemannian manifolds with special holonomy groups. We introduce the notion of holonomy groups on Riemannian manifolds then explain the examples of special holonomy such as Calabi-Yau, Hyper-Kähler, G2 or Spin(7) manifolds. The aim of this course is to understand the fundamental properties of these manifolds.
Be familiar with Riemannian metrics and curvatures.
Be familiar with complex structures."
Kähler manifolds, Calabi-Yau manifolds, Hyper-Kähler manifolds, G2 manifolds, Spin(7) manifolds
|Intercultural skills||Communication skills||Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
This is a standard lecture course. There will be some assignments.
|Course schedule||Required learning|
|Class 1||The following topics will be covered. - Riemannian manifolds and Levi-Civita connections - Holonomy groups - Curvatures - Complex manifolds - Calabi-Yau manifolds and Hyper-Kählermanifolds - Exceptional Holonomy groups"||Details will be provided during each class session.|
To have basic knowledge in the theory of differentiable manifolds.