MMETR Construction of metrics with special holonomies via geometrical flows

Faculty of Science
Spring 2015
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.
The course is also listed under the following terms Spring 2014.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/spring2015/MMETR