Seminar: Introduction to Riemannian Geometry

Sommersemester 2015

Prof. Dr. Anna Wienhard and Dr. Gye-Seon Lee

Time and Location
Thursdays/Fridays 2 - 5 p.m. and INF 294, -112

Next meeting
July 17, at 2 p.m. in INF 294, -112

Office hours
Wednesdays 3 - 5 p.m. in INF 288, 108

Organization meeting
May 28, at 2 p.m. in INF 288, HS 6

Description
The goal of this seminar is to familiarize students with the basic language of and some fundamental theorems in Riemannian geometry. We will introduce the basic concepts of Riemannian geometry, e.g. Riemannian metrics, connections, geodesics, curvature, and Jacobi fields, and thereafter we begin the study of global questions, e.g. the Theorems of Hadamard, Myers and Synge, the Rauch comparison theorem, and the Morse index Theorem. Our main reference is the book "Riemannian Geometry" by Manfredo P.do Carmo. After you skim over the book, you can choose one chapter (or project) you are interested in. During the first half of the semester, students will work on their chapter/project, which they will present during the second half of the semester. Every student is expected to hand in a short report as well.

Prerequisites
This seminar is aimed at students who are interested in differential geometry. Students are expected to have a good knowledge of calculus, a certain familiarity with the differential geometry of surfaces, and properties of covering spaces and of the fundamental group. Interested students from physics are also welcome to attend. The seminar is open for bachelor and master students. The seminar will be taught in English.

Organization
Students who would like to sign up for the seminar should come to the organization meeting or send Gye-Seon an email (lee@mathi.uni-heidelberg.de) and let him know what project you would like to carry out. Once you have agreed on the topic of your project with him, you should contact him to discuss the content of your project in more detail. Please let him help you during the preparation of your presentation.

Schedule

Date	Time	Speaker	Title	Building	Room
July 2	14:15 - 15:15	Carlos	Differentiable manifolds	INF 294	-112
July 9	14:15 - 15:15	Jakob	Riemannian connections
July 10	14:15 - 15:15	Lukas	Geodesics
	15:30 - 16:30	Hyuk Jin	Convex neighborhoods
July 16	14:15 - 15:15	Sören	Curvature
	15:30 - 16:30	Sebastian	Jacobi fields
July 17	14:15 - 15:15	Sven	Hopf-Rinow and Hadamard Theorems
	15:30 - 16:30	Fabian	Spaces of constant curvature

Reference
Manfredo P.do Carmo, Riemannian Geometry, Birkhäuser, 1992.