Differential Geometry II
In the lecture, basic topics in Riemannian Geometry are treated from a theoretical point of view and illustrated with several examples.
Content: A digest of the following topics will be presented:
 Exponential map and HopfRinow theorem
 Connections between curvature und topology (e.g. Myers theorem, HadamardCartan theorem, Klingenberg theorem, rigidity theorems)
 Closed geodesics
 Stokes theorem, cohomology
 Spaces of constant curvature, Lie groups, symmetric and homogeneous spaces
 Conformal geometry, geometric evolution equations and differential equations from geometric analysis
 Basic concepts from differential topology
(19214301)
To achieve regular and active participation it is necessary to visit at least 75% of the offered tutorials and to earn at least 60% of the possible points on the exercise sheets.Type  Lecture with exercise session 

Instructor  Prof. Dr. Konrad Polthier 
Language  English 
Credit Points  10 
Start  Apr 16, 2024  12:00 PM 
end  Jul 18, 2024  02:00 PM 
Time 

Note  Precondition: Differential Geometry I 
Literature
 Wolfgang Kühnel  Differentialgeometrie (English version: Differential Geometry)
 Barrett O'Neill  SemiRiemannian Geometry
 Peter Petersen  Riemannian Geometry

Georg Glaeser, Konrad Polthier  Bilder der Mathematik
Exercise Sheets
Notes
 Lecture 01 (Manifolds)
 Lecture 02 (Vector Fields)
 Lecture 03+04 (Metric)
 Lecture 04+05 (Connections)
 Lecture 06 (Geodesics)
 Lecture 07 (Tensors)
 Lecture 08 (Curvature Tensor)
 Lecture 0910 (JacobiFields)
 Lecture 11+13+14 (Sectional Curvature)
 Lecture 12 (Locally symmetric)
 Lecture 15 (First Fundamental Group)
 Lecture 16+17+18 (Covering Spaces)
 Lecture 18+19 (Symmetric Spaces)
 Lecture 19+20+21 (Lie Groups)
 Script (Adjoint Representation)