MM804: Riemannian geometry and Einstein metrics (5 ECTS)

STADS: 13006801

Level
Master's level course

Teaching period
The course is offered in the autumn semester.
Offered when needed.

Teacher responsible
Email: svensson@imada.sdu.dk

Timetable
There is no timetable available for the chosen semester.

Comment:
Ubegrænset deltagerantal. Kurset kører i 1. kvartal.

Prerequisites:
None

Academic preconditions:
Material from MM512 is assumed known.

Course introduction
The course is an introduction to geometry in arbitrary dimensions and includes both global aspects and applications to mathematical physics.

Expected learning outcome
the end of the course the student should be able to:

• reproduce definitions and results, including their proofs, from differential geometry within the scope of the course syllabus
• apply these results to problems in Riemannian geometry
• relate global expressions with expressions in local coordinates
• explain how the constructions and results in the course are related to
(a) the theory of curves and surfaces in Euclidean space and (b) ideas from theoretical physics

Subject overview
Manifolds, tangent vectors, metrics, connections, curvature, Einstein manifolds, topological consequences of curvature.

Literature

Meddeles ved kursets start.

Syllabus
See syllabus.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
a) Mandatory exercises, pass/fail, internal evaluation by teacher. The exercises must be passed in order to take the oral exam.
b) Oral exam. Danish 7 mark scale, external examiner. There will be 30 minutes preparation for the oral exam.

Terms for re-exam according to the rules decided by the Study Board.

Expected working hours
The teaching method is based on three phase model.

Forelæsninger: 28.
Eksaminatorietimer/opgaveregning: 14.
Educational activities

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.