Wintersemester 2017/2018

Global Analysis I

Content

This course will cover a review of manifolds,vector bundles, vector fields, differential forms, Stokes Theorem and related results (divergence theorem, Gauss’ theorem). We will cover the basic notions of Riemannian geometry, such as metrics on vector bundles, connections and geodesics. Distance and curvature on a Riemannian manifold, submanifolds, the second fundamental form. We will then discuss the Gauss--Bonnett theorem and the relation between curvature and topology. Content sheet

Timetable

Tue 16-18, Hörsaal Physikalische Chemie, Wegelerstr. 12
Wed 12-14, Zeichensaal, Wegelerstr. 10

Exercise tutorials

Mo 10-12, N 0.007 - Neubau, Endenicher Allee 60, tutor: Saskia Roos
Mo 12-14, N 0.003 - Neubau, Endenicher Allee 60, tutor: Thorben Kastenholz

Grading and Exam:

To participate in the exam a 50% score on the assigned exercises is required

First exam: Saturday 03-02-2018, time: 9-11, room: Kleiner Hoersaal, Wegelerstrasse 10.
Klausureinsicht / Post-exam review: Thursday 08-02-2018, 11-12, room N.1009, Endenicher Allee 60 (Neubau).
Second exam: Tuesday 13-03-2018, time: 9-11, room: Kleiner Hoersaal, Wegelerstrasse 10.
Zweite Klausureinsicht / 2nd Post-exam review: Thursday 15-03-2018, 11-12, room 1.028, Endenicher Allee 60.

Literature

John. M. Lee, Riemannian manifolds - an introduction to curvature, Springer, 1997;
John. M. Lee, Introduction to smooth manifolds, Springer, 2003.

Bram Mesland