Differential Geometry

The lecture course Differential Geometry will provide a basic introduction to the theory of smooth manifolds, Riemannian and Poisson geometry, and the theory of fibre bundles.
The topics covered will include

• Manifolds, smooth maps and vector fields
• Differential forms
• Riemannian manifolds
• Symplectic and Poisson manifolds
• Lie groups and Lie algebras
• Principal fibre bundles
• Vector bundles
• Connections and curvature

Applications in theoretical physics (classical mechanics, general relativity, gauge theory) will be used as illustration and motivation if wanted.

The topics are fairly standard and hence covered in many textbooks. A small selection of possible sources can be found below.

Reading List Differential Geometry

• Ilka Agricola, Thomas Friedrich: "Globale Analysis"
• Helga Baum: "Eichfeldtheorie"
• David Bleecker: "Gauge Theory and Variational Principles"
• Nigel Hitchin: "Differential Geometry"
• Klaus Jänich: "Vektoranalysis"
• David Sattinger, Oliver Weaver: "Lie Groups and Algebras with Applications to Physics, Geometry and Mechanics"

Time Table