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.

Content

Keywords

Differential geometry; Riemannian metric; Curvature tensor; geodesics

Learning Prerequisites

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

Resources

Virtual desktop infrastructure (VDI)

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

 

Ressources en bibliothèque

Moodle Link

Prerequisite for

Differential Geometry IV - General Relativity

In the programs

  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Differential geometry III - Riemannian geometry
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks

Reference week

 MoTuWeThFr
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

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