Semi-Riemannian manifolds, semi-Riemannian submanifolds, Riemannian and Lorentzian geometry, constructions of semi-Riemannian manifolds, symmetry and constant curvature, isometries, calculus of varations.
FSF3670 Semi-Riemannian Geometry 1 7.5 credits
Information per course offering
Course offerings are missing for current or upcoming semesters.
Course syllabus as PDF
Please note: all information from the Course syllabus is available on this page in an accessible format.
Course syllabus FSF3670 (Autumn 2018–)Headings with content from the Course syllabus FSF3670 (Autumn 2018–) are denoted with an asterisk ( )
Content and learning outcomes
Course contents
Intended learning outcomes
After the course, the student should have a sufficiently deep knowledge of semi-riemannian geometry to be able to start working on research projects in the area.
Literature and preparations
Specific prerequisites
Prerequisite for the course is a strong knowledge of differential geometry (differential manifolds, tensors, differential forms) corresponding for example to the advanced level course SF2722 “Differential geometry”.
Literature
The course is primarily based on the book
- O'Neill, Barrett “Semi-Riemannian Geometry With Applications to Relativity”, Academic Press, Orlando 1983.
Also used in the course are the books:
Petersen, Peter, “Riemannian geometry”. Third edition. Graduate Texts in Mathematics, 171. Springer, Cham, 2016.
Sakai, Takashi. “Riemannian geometry”. Translations of Mathematical Monographs, 149. American Mathematical Society, Providence, RI.
Besse, Arthur L. “Einstein manifolds”. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 10. Springer-Verlag, Berlin, 1987.
Examination and completion
Grading scale
P, F
Examination
- HEM1 - Home assignments, 7.5 credits, grading scale: P, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
If the course is discontinued, students may request to be examined during the following two academic years.
Homework assignments and oral test or presentation.
Other requirements for final grade
Homework assignments completed, and satisfactory performance at oral test or presentation.
Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information
Course room in Canvas
Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.
Offered by
Education cycle
Third cycle