Course content

Introduction to Riemannian geometry. Affine connections. Curvature. Calculus of variations applied to the connection between topology and curvature. Submanifolds, Fundamental Theorem. Introduction to more general concepts of curvature (Cartans repère mobile or Ehresmann-connections).

Learning outcome

To give a proper background in differential geometry for applications in theoretical physics and for futher studies in geometry/geometrical analysis.

Admission

PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.

If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.

PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.

Prerequisites

Recommended previous knowledge

MAT4520 – Manifolds.

Overlapping courses

15 credits with MA 392.

*The information about overlaps is not complete. Contact the Department for more information if necessary.

Teaching

4 hours of lectures per week. Taught according to demand and resources.

If few students apply for the course, it may be given as self-tuition with one hour of common academic supervision each week.

Examination

Oral exam.

In addition, each phd student is expected to give a one hour oral presentation on a topic of relevance (chosen in cooperation with the lecturer). The presentation has to be approved by the lecturer for the student to be admitted to the final exam.

Examination support material

No examination support material is allowed.

Language of examination

Subjects taught in English will only offer the exam paper in English.

You may write your examination paper in Norwegian, Swedish, Danish or English.

Grading scale

Grades are awarded on a pass/fail scale. Read more about the grading system.

Explanations and appeals

Resit an examination

Students who due to illness or other valid reason of absence were unable to si