401-3532-08L  Differential Geometry II

SemesterSpring Semester 2021
LecturersW. Merry
Periodicityyearly recurring course
Language of instructionEnglish



Courses

NumberTitleHoursLecturers
401-3532-08 VDifferential Geometry II
At least in February and March and 1 April online via Zoom.
4 hrs
Mon14:15-16:00HG D 1.1 »
Thu10:15-12:00CAB G 11 »
W. Merry
401-3532-08 UDifferential Geometry II
Groups are selected in myStudies.
Fri 9-10 or Fri 10-11
1 hrs
Fri09:15-10:00HG E 1.1 »
10:15-11:00HG E 1.1 »
W. Merry

Catalogue data

AbstractThis is a continuation course of Differential Geometry I.

Topics covered include:

- Connections and curvature,
- Riemannian geometry,
- Gauge theory and Chern-Weil theory.
Objective
Lecture notesI will produce full lecture notes, available on my website:

Link
LiteratureThere are many excellent textbooks on differential geometry.

A friendly and readable book that contains everything covered in Differential Geometry I is:

John M. Lee "Introduction to Smooth Manifolds" 2nd ed. (2012) Springer-Verlag.

For Differential Geometry II, the textbooks:

- S. Kobayashi, K. Nomizu "Foundations of Differential Geometry" Volume I (1963) Wiley,
- I. Chavel, "Riemannian Geometry: A Modern Introduction" 2nd ed. (2006), CUP,

are both excellent. The monograph

- A. L. Besse "Einstein Manifolds", (1987), Springer,

gives a comprehensive overview of the entire field, although it is extremely advanced. (By the end of the course you should be able to read this book.)
Prerequisites / NoticeFamiliarity with all the material from Differential Geometry I will be assumed (smooth manifolds, Lie groups, vector bundles, differential forms, integration on manifolds, principal bundles and so on). Lecture notes for Differential Geometry I can be found on my website.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits10 credits
ExaminersW. Merry
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.

Groups

401-3532-08 UDifferential Geometry II
GroupsG-01
Fri09:15-10:00HG E 1.1 »
G-02
Fri10:15-11:00HG E 1.1 »

Restrictions

There are no additional restrictions for the registration.

Offered in

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