MATH-344 / 5 credits

Teacher: Moschidis Georgios

Language: English

## Summary

This course will serve as a first introduction to the geometry of Riemannian manifolds, which form an indispensible tool in the modern fields of differential geometry, analysis and theoretical physics.

## Keywords

Differential geometry; Riemannian metric; Curvature tensor; geodesics

## Required courses

Introduction to differentiable manifolds (MATH-322), Analysis I-IV.

## Important concepts to start the course

Differentiable manifold, tangent space, vector fields, tensors.

## Learning Outcomes

By the end of the course, the student must be able to:

• Define the central objects of Riemannian geometry (Riemannian metric, geodesics etc.)
• Use these objects together with the fundamental identities satisfied by them to solve problems
• Prove the main theorems appearing in the course

## Transversal skills

• Assess progress against the plan, and adapt the plan as appropriate.
• Demonstrate a capacity for creativity.
• Demonstrate the capacity for critical thinking
• Access and evaluate appropriate sources of information.

## Teaching methods

2h lectures + 2h exercises

## Expected student activities

Attending lectures and solve problems sheets; interacting in class; revise course content.

## Assessment methods

Final exam.
Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

## Supervision

 Office hours No Assistants Yes Forum Yes

No

## Bibliography

There are many introductory books on Riemannian geometry, unfortunately most of them intended for an audience of graduate students. We will follow closely the exposition of the following two books (which are also available at the EPFL library):
do Carmo, Manfredo; Riemannian geometry. Birkhäuser Boston, Inc., Boston, MA, 1992
Petersen, Peter; Riemannian geometry. Springer-Verlag New York 2006

## Notes/Handbook

Written notes will be provided

## In the programs

• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Introduction to differential geometry
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks

## Reference week

 Mo Tu We Th Fr 8-9 9-10 10-11 11-12 12-13 13-14 CM013 14-15 15-16 16-17 MAA112 17-18 18-19 19-20 20-21 21-22

Wednesday, 16h - 18h: Lecture MAA112

Friday, 13h - 15h: Exercise, TP CM013