Entry requirements

120 credits including 90 credits Mathematics. Differential topology participation. Proficiency in English equivalent to the Swedish upper secondary course English 6.

Learning outcomes

On completion of the course, the student should be able to:

• define the various geometrical and algebraic concepts that are introduced in the course, and be able to use and interpret them i specific examples,
• use and formulate central theorems in Riemannian geometry and Topology, and be able to give an account of their proofs,
• use the theory, methods and techniques of the course to solve problems.

Content

Parallel transport, connections, covariant derivate and curvature.Levi-Civita connections. Second fundamental form and Gauss equations. Geodesics: first and second variations of arc length, Jacobi fields, conjugate points andcomparison theorems. Existence theorems of geodesics and spaces of curves in Riemannian manifolds.

Instruction

Lectures and problem solving sessions.

Assessment

Written assignments during the course combined with an oral follow-up examination at the end of the course (10 credits).

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.

Other directives

The course may not be included in the same higher education qualification as Riemannian Geometry (1MA093) or Riemannian Geometry (1MA196).