Geometry University of Bordeaux
Science and Technology
This course is an introduction to Riemannian Geometry, and will_
prepare for the course "K_hler Geometry" that will take place during
the second semester.
> Lectures and practical work:
- 57 course hours.
- 200 hours of personal study.
> The following topics will be discusses:
- Differentiable manifolds, tangent bundles.
- Vector field, derivations.
- Riemannian metric, covariant derivative,geodesics.
- 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
- 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.
> 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.
Exams take place in December.
12 weeks (Fall Semester)
- 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/]
Site for Inquiry