Geometry University of Bordeaux
Course Overview
This course is an introduction to Riemannian Geometry, and will prepare for the course "Kähler Geometry" that will take place duringthe second semester.
Learning Achievement
Competence
Course prerequisites
> 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.
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 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.
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, 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.bavard@u-bordeaux.frChristine Bachocchristine.bachoc@u-bordeaux.fr