PřF:MMETR Metrics with spec. holonomies - Course Information
MMETR Construction of metrics with special holonomies via geometrical flows
Faculty of ScienceSpring 2014
- Extent and Intensity
- 4/0. 1 credit(s). Type of Completion: k (colloquium).
- Teacher(s)
- Dr. Evgeny Malkovich, PhD (lecturer), doc. Anton Galaev, Dr. rer. nat. (deputy)
- Guaranteed by
- doc. Anton Galaev, Dr. rer. nat.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. Anton Galaev, Dr. rer. nat.
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Prerequisites
- Be familiar with the notion of a smooth manifold, tensor fields, linear connections
- Course Enrolment Limitations
- The course is offered to students of any study field.
- Course objectives
- Few years ago in theoretical physics it was very popular to find compact Calabi-Yau spaces and manifolds with exceptional holonomies G_2 and Spin(7). Such metrics themselves are of interest in contemporary differential geometry. The main purpose of the lectures is to explain some techniques that can be used to construct metrics with SU(n), G_2 and Spin(7) holonomies. It is turned out that some classical metrics (for example Egushi-Hanson metric) can be obtained as the certain solutions of generalized geometrical flows.
- Syllabus
- Riemannian connections and holonomies
- 3-Sasakian manifolds
- Orbifolds, Riemannian cones
- Resolutions of the conical singularities and behaviour of the metric as time goes to infinity
- Topology of the spaces with found metrics
- Geometrical flows and classical metrics
- Language of instruction
- English
- Further Comments
- The course is taught only once.
The course is taught: in blocks.
- Enrolment Statistics (Spring 2014, recent)
- Permalink: https://is.muni.cz/course/sci/spring2014/MMETR