Geometry University of Bordeaux
This course is an introduction to Riemannian Geometry, and will prepare for the course "Kähler Geometry" that will take place duringthe second semester.
> Applicants should: - Have completed, with good results, a Bachelor of science degree inMathematics or equivalent with a special focus on Algebra, Geometryand Number Theory. - Have thorough proficiency in written and spoken English.
Exams take place in December.
> 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 Riemanniangeometry,North-Holland Publishing Company, 1975 - M. Do Carmo, Riemannian Geometry, Mathematics: Theory andApplications, Birkh »auser, 1992 - S. Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry, Springer-Verlag, secondedition, 1993.
> Lectures and practical work: - 57 course hours. - 200 hours of personal study.
Online Course Requirement
- This course is part of the ALGANT Joint Master Program. - For further information on the program structure, partnerinstitutions, scholarship opportunities, etc., please visit: ALGANTErasmus Mundus. [http://algant.eu/]Duration: 12 weeks (Fall Semester)Language of instruction: EnglishMode of delivery: Face-to-face teaching
Site for Inquiry
Please inquire about the courses at the address below.
Contact person: Christopher Bavardchristopher.firstname.lastname@example.orgChristine Bachocchristine.email@example.com