Differential Geometry (Summer Semester 2019)
- Lecturer: Prof. Dr. Wilderich Tuschmann (Spokesman of the Institute)
- Classes: Lecture (0100300), Problem class (0100310)
- Weekly hours: 4+2
|Lecture:||Wednesday 11:30-13:00||SR 1.067|
|Thursday 11:30-13:00||SR 0.014|
|Problem class:||Monday 15:45-17:15||SR 2.067|
|Lecturer, Problem classes||Prof. Dr. Wilderich Tuschmann (Spokesman of the Institute)|
|Office hours: by appointment - please contact me by email;|
|Room 1.002 Kollegiengebäude Mathematik (20.30)|
|Email: firstname.lastname@example.org||Problem classes||Dr. Jan-Bernhard Kordaß|
|Office hours: By appointment.|
|Room 1.021 Kollegiengebäude Mathematik (20.30)|
- The first exercise class will take place on Monday, 29 April
- The exercise class has been moved from Wednesday to Monday at 3.45 p.m.
Differential geometry is one of the most research-intensive areas of mathematics in recent decades. It has a long tradition that traces its development back well over a century. Its current prominence stems from its position at the crossroads of many active fields such as: topology, metric geometry, analysis, partial differential equations, Lie and other forms of group theory. Its influence spreads well beyond the confines of pure mathematics to interact with theoretical physics and extends to a multitude of practical applications as diverse as engineering, robotics and computer vision.
The course will provide a thorough introduction to the basics of modern differential geometry, such as manifolds, tensors, bundles, Riemannian metrics, linear connections, covariant derivatives, parallel transport, geodesics, and curvature.
Exercise sheets will be published weekly on the Ilias platform.
W. M. BOOTHBY, An introduction to differentiable manifolds and Riemannian geometry. Second edition. Pure and Applied Mathematics, 120. Academic Press, Inc., Orlando, FL, (1986).
J. JOST, Riemannian geometry and geometric analysis. Sixth edition. Universitext. Springer, Heidelberg, (2011).
S. Gallot, D. Hulin & J. Lafontaine, Riemannian geometry. Third edition. Universitext, Springer-Verlag, Berlin (2004)
T. Sakai, Riemannian geometry. Translations of Mathematical Monographs 149, American Mathematical Society, Providence, RI (1996)