From 2 November 2020, the autumn semester 2020 will take place online. Exceptions: Courses that can only be carried out with on-site presence. Please note the information provided by the lecturers via e-mail.

401-3532-08L  Differential Geometry II

SemesterSpring Semester 2016
LecturersM. Burger
Periodicityyearly recurring course
Language of instructionEnglish

Catalogue data

AbstractThe aim of this course is to give an introduction to Riemannian Geometry and modern metric geometry.
ObjectiveRiemannian Geometry, metric geometry.
ContentThe aim of this course is to give an introduction to Riemannian Geometry and modern metric geometry. We will present the basics on affine and riemannian connections, discuss existence and properties of geodesics; then we proceed to the central concept of riemannian curvature tensor and its various avatars, like sectional curvature and scalar curvature. We will then move to Topogonov's comparison theorems. This constitutes the bridge with metric geometry and the modern notion of negative curvature, which applies to singular spaces, and constitutes the topic of the second part of this course.
Lecture notesWill be made available.
LiteratureM.P. do Carmo, "Riemannian Geometry", Birkhauser, 1992

M. Bridson, A. Haefliger, "Metric Spaces of Non-Positive Curvature",
Springer 1999.
Prerequisites / NoticePrerequisite are the sections concerning manifolds and tangent bundles of the Differential Geometry I course, Fall Semester 2015.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits10 credits
ExaminersM. Burger
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationoral 30 minutes
Additional information on mode of examinationLanguage of examination: English or German / Prüfungssprache: Deutsch oder Englisch
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

No public learning materials available.
Only public learning materials are listed.


401-3532-00 VDifferential Geometry II4 hrs
Mon13-15HG D 3.2 »
Wed13-15HG E 1.2 »
M. Burger
401-3532-00 UDifferential Geometry II1 hrs
Fri08-09HG E 1.1 »
09-10HG E 1.1 »
10-11HG E 1.1 »
12-13HG E 1.1 »
M. Burger


No information on groups available.


There are no additional restrictions for the registration.

Offered in

Doctoral Department of MathematicsGraduate SchoolWInformation
High-Energy Physics (Joint Master with EP Paris)Optional Subjects in MathematicsWInformation
Mathematics BachelorCore Courses: Pure MathematicsWInformation
Mathematics MasterCore Courses: Pure MathematicsWInformation
Physics BachelorSelection of Higher Semester CoursesWInformation
Physics MasterSelection: MathematicsWInformation