Course Overview

This course is an introduction to Riemannian Geometry, and will 
prepare for the course "Kähler Geometry" that will take place during
the second semester.

Learning Achievement

Competence

Course prerequisites

> Applicants should:

- Have completed, with good results, a Bachelor of science degree in
Mathematics or equivalent with a special focus on Algebra, Geometry
and Number Theory.
- Have thorough proficiency in written and spoken English.

Grading Philosophy

Exams take place in December.

Course schedule

> The following topics will be discusses:

- Differentiable manifolds, tangent bundles.
- Vector field, derivations.
- Riemannian metric, covariant derivative,geodesics.
- Curvatures
- Variation formulas for arc length andenergy,  Jacobi field
- Synge theorem, Hadamard-Cartan theorem, Myerstheorem
- Spaces of constant curvature, Cartan theorem
- Volume, Bishop-Gromov comparison theorem
- Rauch comparison theorem, Toponogov theorem

> Bibliography:

- J. Cheeger and  D. Ebin,  Comparison theorems in Riemannian
geometry,North-Holland Publishing Company, 1975
- M. Do Carmo, Riemannian Geometry, Mathematics: Theory and
Applications, Birkh »auser, 1992
- S. Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry, 
Springer-Verlag, secondedition, 1993.

Course type

> Lectures and practical work: - 57 course hours. - 200 hours of personal study.

Online Course Requirement

Instructor

Other information

- This course is part of the ALGANT Joint Master Program.

- For further information on the program structure, partner
institutions, scholarship opportunities, etc., please visit: ALGANT
Erasmus Mundus. [http://algant.eu/]

Duration: 12 weeks (Fall Semester)

Language of instruction: English
Mode of delivery: Face-to-face teaching

Site for Inquiry