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Course Jukebox

Course Detail

School
College of Science and Technology
Study
Mathematics
Campus
College of College of Science and Technology/Campus Talence
Course Offering Term
September - January
Weekday and Period
Capacity
Credits
9 ECTS
Standard Academic Year
Semester 3 (2nd year)
Language
English
Course Number

Geometry University of Bordeaux

Responsible Organization

College of Science and Technology

Mathematics

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

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 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

12 weeks (Fall Semester)

Lectures and practical work:

- 57 course hours.

- 200 hours of personal study.

Instructor

Laurent Bessieres

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/]

Face-to-face teaching

Site for Inquiry

Please inquire about the courses at the address below. Christine Bachoc/christine.bachoc@u-bordeaux.fr