This course is discontinued

Schedule, syllabus and examination date

Choose semester

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.


Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.


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.


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


Oral exam.

One compulsory assignment needs to be passed within given deadlines to be allowed to take the final exam.

Rules for compulsory assignments at the Department of Mathematics.

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 scale from A to F, where A is the best grade and F is a fail. 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 sit for their final exams may apply for participation in deferred examinations. Deferred examinations are arranged either later in the same semester or early in the semester following the exam in question. Documentation of valid reasons for absence from the regular exam must be submitted upon application to participate in deferred examinations.

Students who have failed an exam, who withdraw during an exam, and students who wish to retake an exam to achieve a better grade may not participate in deferred exams, but may retake the exam when it is regularly scheduled.

Information about deferred and new examination (also called repeat examination) is found here

More information about examination at the Faculty of Mathematics and Natural Sciences can be found here

Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

Special examination arrangements

Application form, deadline and requirements for special examination arrangements.


The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.

Facts about this course






Spring 2009

This course was held for the last time Spring 2009. MAT4590 – Differential Geometry will cover the same material.


Spring 2009

Teaching language


The course is given in English. If no students have asked for the course in English within the first lecture, it may be given in Norwegian.