Topics of the lecture will be:

• Curves and surfaces in Euclidean space
• Metrics and (Riemannian) manifolds
• Surface tension and notions of curvature
• Vector fields, tensors, covariant derivative
• Geodesic curves, exponential map
• Gauß-Bonnet theorem, curvature and topology
• Connection to discrete differential geometry

Prerequisits: Analysis I, II and Linear Algebra I, II

Literature

• W. Kühnel: Differentialgeometrie:Kurven - Flächen - Mannigfaltigkeiten, Springer, 2012
• M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall
• J.-H. Eschenburg, J. Jost: Differentialgeometrie und Minimalflächen, Springer, 2014
• C. Bär: Elementare Differentialgeometrie, de Gruyter, 2001

For further information, see Lecture Homepage.