Universität Regensburg   IMPRESSUM   DATENSCHUTZ
Fakultät für Mathematik Universität Regensburg

Hinweis Bitte informieren Sie sich auf den jeweiligen GRIPS-Seiten über den digitalen Ablauf der Lehrveranstaltungen.

English Note For our digital courses all relevant information can be found on the appropriate GRIPS sites.

Differential Geometry I
Semester
WiSe 2020 / 21

Lecturer
Clara Löh

Type of course (Veranstaltungsart)
Vorlesung

Contents
Differential geometry is the study of geometric objects by analytic means. Geometric objects in this context usually are Riemannian manifolds, i.e., smooth manifolds with a Riemannian metric. This allows to define lengths, volumes, angles, ... in the language of (multilinear) analysis. A central concern of differential geometry is to define and compare (intrinsic) notions of curvature of spaces. A particularly fascinating aspect is that many local curvature constraints are reflected in the global shape.

Differential geometry has various applications in the formalisation of Physics, in medical imaging, and also in other fields of theoretical mathematics. For example, certain phenomena in group theory and topology can only be understood via the underlying geometry.

In this course, we will introduce basic notions of differential geometry. This includes, in particular, the Riemannian curvature tensor, sectional curvature, Ricci curvature, and scalar curvature. Moreover, we will study some first global obstructions to curvature constraints.

If all participants agree, this course can be held in German; solutions to the exercises can be handed in in German or English.

Recommended previous knowledge
All participants should have a firm background in Analysis I/II, in Linear Algebra I/II, in basic group theory (as covered in the lectures on Algebra), and in Analysis IV (e.g., as in Analysis auf Mannigfaltigkeiten; Prof. Ammann, SS 2020).

Time/Date
Wed 8:30--10:00, Thu 10:15--12:00

Location
digital

Course homepage
http://www.mathematik.uni-r.de/loeh/teaching/diffgeo_ws2021
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration
  • Preliminary registration for the organisation of exercise classes: at the end of the previous
    semester via EXA or LSF (see announcement by the department)
  • Registration for the exercise classes: via GRIPS, during the first week
  • Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)
  • Successful participation in the exercise classes: 50% of the credits, presentation of a
    solution in class
Examination (Prüfungsleistungen)
  • Oral exam: Duration: 25 minutes, Date: individual, re-exam: Date: individual
Regelungen bei Studienbeginn vor WS 2015 / 16
  • Benotet:
    • O. g. Studienleistung und o. g. Prüfungsleistung; die Note ergibt sich aus der Prüfungsleistung
  • Unbenotet:
    • O. g. Studienleistung
Modules
BV, MV, MGAGeo

ECTS
9