Universität Regensburg   IMPRESSUM   DATENSCHUTZ
Fakultät für Mathematik Universität Regensburg
Differential geometry II
Semester
SoSe 2022

Lecturer
Ulrich Bunke

Type of course (Veranstaltungsart)
Vorlesung

German title
Differentialgeometrie II

Contents
In this second part of the course we will investigate Riemannian manifolds in greater detail. We study how properties of the curvature tensor determine global properties of the Riemannian manifold as a metric space. In particular we will show Hadamard's theorem stating that negatively curved simply connected complete manifolds are homeomorphic to Euclidean spaces and that complete manifolds with positive Ricci-curvature have bounded diameter. We will consider symmetric spaces as an interesting class of examples of Riemannian manifolds. We will also consider further geometric structures on Riemannian manifolds, e.g. complex structures. If time permits we will do first steps towards global analysis by considering properties of the Laplace operator. The parallel seminar on Morse theory might be an interesting add-on for participants of the course.

Literature
Will be given in the lecture course.

Recommended previous knowledge
manifolds and Riemannian metrics
fibre bundle language
connections on vector bundles


Time/Date
Mo, Do 10-12

Location
MA 102

Course homepage
GRIPS
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration
  • Registration for the exercise classes: via GRIPS
  • Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)
  • Successful participation in the exercise classes: 50% of the exercises, successful presentation
    of solutions
Examination (Prüfungsleistungen)
  • Oral exam: Duration: 25 min, Date: N.N., re-exam: Date:
Modules
BV, MV, MGAGeo, LA-GyGeo

ECTS
9