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- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Hattori Kota
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Intensive ()
- Group
- -
- Course number
- MTH.E634
- Credits
- 2
- Academic year
- 2019
- Offered quarter
- 4Q
- Syllabus updated
- 2019/3/18
- Lecture notes updated
- -
- Language used
- English
- Access Index
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Course description and aims
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.
Student learning outcomes
Be familiar with Riemannian metrics and curvatures.
Be familiar with complex structures."
Keywords
Kähler manifolds, Calabi-Yau manifolds, Hyper-Kähler manifolds, G2 manifolds, Spin(7) manifolds
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Class flow
Regular lecture course format with homework exercises
Course schedule/Required learning
| 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" | to be specified in each lecture |
Textbook(s)
none in particular
Reference books, course materials, etc.
none
Assessment criteria and methods
Assignments (100%).
Related courses
- MTH.B301 ： Geometry I
- MTH.B302 ： Geometry II
- MTH.B331 ： Geometry III
- MTH.B341 ： Topology
- MTH.C301 ： Complex Analysis I
Prerequisites (i.e., required knowledge, skills, courses, etc.)
To have basic knowledge in the theory of differentiable manifolds
