Universit├Ąt Regensburg   IMPRESSUM   DATENSCHUTZ
Fakultät für Mathematik Universität Regensburg
Differential Geometry I
Semester
WiSe 2023 / 24

Lecturer
Bernd Ammann

Type of course (Veranstaltungsart)
Vorlesung

German title
Differentialgeometrie I

Contents
This lecture is an introduction to differential geometry, more precisely to semi-Riemannian manifolds, their curvature and global properties.
The main topic are Riemannian metrics on manifolds. The simplest examples are surfaces in Euclidean space ℝ3. Such surfaces may be intrinsically curved, as e.g. the sphere. Or they may only be extrinsically curved, as e.g. a cylinder -- which may be cut by a "scissor" and then this surface is isometric to an open set of a plane.
The goal is to understand not only surfaces, but similar curvature quantities in arbitrary dimensions and codimensions, a generalization going back to work of Bernhard Riemann. Very similar structures were later used by Einstein and others in order to get a mathematical framework to describe general relativity. The theory is still a very active area in mathematics and theoretical physics. The lecture will be continued in the summer term.

Literature
C. Bär, Differential Geometry, Unpublished Lecture Notes, to access click on this link,
Further literature on the web page

Recommended previous knowledge
  • Analysis I, II and IV
  • Linear Algebra I and II


Time/Date
Monday and Friday, 10-12

Location
M102

Course homepage
https://ammann.app.uni-regensburg.de/lehre/2023w_diffgeo1
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration
  • Registration for the exercise classes: In the first week of the semester in the lecture
  • Please register on the GRIPS system. We will send out additional information and emails via
    GRIPS
  • Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)
  • Successful participation in the exercise classes:
Examination (Prüfungsleistungen)
  • Oral exam: Duration: 30 minutes , Date: individual arrangements, re-exam: Date:
Modules
BV, MV, MGAGeo, LA-GyGeo

ECTS
9