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 semiRiemannian manifolds, their curvature and global properties.
The main topic are Riemannian metrics on manifolds. The simplest examples are surfaces in Euclidean space ℝ^{3}. 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Literature C. Bär, Differential Geometry, Unpublished Lecture Notes, to access click on this link,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, 1012
Location M102
Course homepage https://ammann.app.uniregensburg.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, reexam: Date:
Modules BV, MV, MGAGeo, LAGyGeo
ECTS 9

