MATH-344 / 5 crédits

Enseignant: Moschidis Georgios

Langue: Anglais

## 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

Differential Geometry II - Smooth manifolds, Analysis I-IV.

## Important concepts to start the course

Differentiable manifold, tangent-cotangent space, vector fields.

## 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

## 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 No

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 book:
do Carmo, Manfredo; Riemannian geometry. Birkhäuser Boston, Inc., Boston, MA, 1992.

We will sometimes use material from:

Petersen, Peter; Riemannian geometry. Springer-Verlag New York 2006.

Both manuscripts are available at the EPFL library.

Ressources en bibliothèque

## Prerequisite for

Differential Geometry IV - General Relativity

## Dans les plans d'études

• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Differential geometry III - Riemannian geometry
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines

## Semaine de référence

 Lu Ma Me Je Ve 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

Mercredi, 16h - 18h: Cours MAA112

Vendredi, 13h - 15h: Exercice, TP CM013

## Cours connexes

Résultats de graphsearch.epfl.ch.