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Course Jukebox

Course Jukebox

Course Detail

School
Science and Technology
Study
Mathematics
Campus
College of Science and Technology
Course Offering Term
September - December
Weekday and Period
Capacity
Credits
9 ECTS
Standard Academic Year
Semester 3
Language
English
Course Number

Geometry University of Bordeaux

Responsible Organization

Science and Technology

Mathematics

Course Overview

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.

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)

Course type

Face-to-face teaching

Instructor

Laurent Bessieres,laurent.bessieres@u-bordeaux.fr

Other information

2018

- 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

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