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Wintersemester 2015/2016

Differential Geometry (TMP)

Gerasim Kokarev (Mathematisches Institut der LMU) and
Peter Mayr (Fakultät für Physik der LMU)

Course description:
This course gives an introduction to basic concepts in geometry, which are essential to a number of other mathematical and physical disciplines.

It is oriented on students in Mathematics and Physics and covers the module "Differential Geometry" in the Master Programme in Theoretical and Mathematical Physics (TMP) as well as the Master Mathematics Programme.

Pre-requisites:
Modules covering Linear Algebra, Several Variable Calculus, and Point-Set Topology.

Lectures schedule:
Lectures will be given in English twice a week, 12.00-14.00 Tue and 12.00-14.00 Thu, Room B 006

Office hours: 14.00-16.00 Tue, Room B308.

Course outline:
The course includes the standard introductory material on manifolds, vector bundles, Lie groups and Lie algebras; vector fields and flows; differential forms and tensor fields; Riemannian metrics, connections, curvature.

Reading list:
1. Conlon, L. Differentiable manifolds: a first course. Birkhäuser Advanced Texts: Basler Lehrbücher. 1993. xiv+395 pp.1
2. Dubrovin, B. A.; Fomenko, A. T.; Novikov, S. P. Modern geometry - methods and applications. Part II. The geometry and topology of manifolds. Graduate Texts in Mathematics, 104. Springer-Verlag, New York, 1985. xv+430 pp.2
3. Warner, F. Foundations of differentiable manifolds and Lie groups. Graduate Texts in Mathematics, 94. Springer-Verlag, New York-Berlin, 1983. ix+272 pp.

Exercise classes (Übungen):
Exercise classes are given by Rui Coelho and Giovanni Placini; all relevant information can be found at http://www.math.lmu.de/~mcoelho/WS1516/manifolds.html

There will be a few exercise groups preliminary arranged for 8.00-10.00 Mon, 16.00-18.00 Mon, and 12.00-14.00 Fri; all in Room B047. Please come to the first group meeting to meet a person who will do the classes.

Students are encouraged to attend exercise classes and do as many problems in the Exercise Sheets as possible, since they comprise an important part of the course and the problems similar to those discussed are likely to appear on the exam.

Mid-Term Test:
The mid-term test will hold on 15 Dec, Tuesday, Room B006 at 12.00-14.00. Please bring your student ID along with a photo ID, and make sure that you arrive before 12.00am.

The results of the mid-term test are available now. PDF <expired link>

Final Exam:
The exam will hold on 11 Feb, Thursday, Room B138 at 12.15-14.15. Please bring your student ID along with a photo ID, and make sure that you arrive at 12.00.

The results of the final exam are available now. PDF

Resit (Make-up Exam):
The purpose of a resit is to give a second chance to students who failed the scheduled exam or to allow students, with legitimate reasons for missing the scheduled exam, to fulfill the requirements of the course.

The second exam will hold on 6 Apr, Wednesday, Room B139 at 9.15-11.15. Please bring your student ID along with a photo ID, and make sure that you arrive at 9.00.

Footnotes:
1. There is also a second edition of this book: Conlon, L. Differentiable manifolds. Second edition. Birkhäuser Advanced Texts: Basler Lehrbücher. 2001. xiv+418 pp.
2. A similar more up-to-date text is: Novikov, S. P.; Taimanov, I. A. Modern geometric structures and fields. Graduate Studies in Mathematics, 71. American Mathematical Society, Providence, RI, 2006. xx+633 pp.

http://www.mathematik.uni-muenchen.de/~kokarev/teaching/ws15_16.html
Last modified: 11 Jan 2016