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401-3589-75L 4 Credits DR , MSC D-MATH

Introduction to Conformal Geometry

Lecturers & Examiners: Dr. Dorian Martino
VVZ CR n/a

Last Updated: 2026-06-01 11:30:59

Abstract

Conformal geometry is the study of geometric properties induced by the measure of angles. Conformal transformations have a surprisingly rich behavior with a strong link to Lorentzian geometry. In this course, we will develop this point of view, providing a generic study of conformally invariant properties.

Objective

By the end of the course, the students will be familiar with the Weyl tensor, Kuiper, Obata and Liouville theorems, Möbius geometry and tractor calculus.

Content

In a first part, we will introduce the Weyl tensor, present Kuiper theorem and study properties of conformally flat manifolds. In a second part, we will introduce the Lorentzian geometry and give applications to some problems of calculus of variations arising in geometry and physics such as Willmore surfaces and Bach-flat manifolds.

Resources

Lecture Notes

Lecture notes will be available.

Literature

Udo Hertrich-Jeromin: Introduction to Möbius differential geometry. Kulkarni-Pinkall (editors): Conformal geometry. Curry-Gover: An introduction to conformal geometry and tractor calculus, with a view to applications in general relativity (lecture notes).

General Information

Language
English
Levels
DR , MSC

Examination

Type
session examination
Mode
oral 20 minutes
The exam is only offered in the Winter 2025/26 and Summer 2026 examination sessions.

Course Components

Type Title Time & Place Hours
lecture Introduction to Conformal Geometry
  • Thu 14:15-16:00 (HG E 22)
  • 18.09 Date 14:15-16:00 (LFW C 5)
2 h weekly

Offered In