The lecture will introduce selected concepts from differential geometry and their role in solving current application problems.
The topics include curvature measures, geometric flows, minimal surfaces, harmonic mapping, parallel transport, branched coverings, as well as their discretization and implementation.
Practical problems come for example from the fields of geometric design, geometry processing, visualization, materials science, medicine, architecture.

To achieve regular and active participation it is necessary to visit at least 75% of the offered tutorials (see StO/PO 2018 (Master, 00280c)) and to earn at least 60% of the possible points on the exercise sheets.

Differential geometry I

• Horst Knörrer - Geometrie
• Wolfgang Kühnel - Differentialgeometrie (English version: Differential Geometry)
• Barrett O'Neill - Semi-Riemannian Geometry
• Blaine Lawson - Complete Minimal Surfaces in S3
• Paul Petersen - Riemannian Geometry
• H. Karcher - Introduction to Conjugate Plateau Constructions
• Robert Osserman - A Survey of Minimal Surfaces
• James R. Munkres - Elements of Algebraic Topology

Exercise Sheets

• Sheet 01
• Sheet 02
• Sheet 03
• Sheet 04
• Sheet 05 (Version 2)
• Sheet 06 (Version 2)
• Sheet 07 (Version 2)
• Sheet 08
• Sheet 09
• Sheet 10
• Sheet 11 (Version 2)
• Sheet 12
• Sheet 13
• Sheet 14 (Version 2)

Slides

• Slides on Branched Covering Surfaces (Part1)
• Slides on Branched Covering Surfaces (Part2)
• Slides on Vibrations of Geometric Shapes
• Slides on Boundary Senitive Hodge Decompositions (Short Version)
• Slides on Boundary Senitive Hodge Decompositions (Long Version)
• Slides on Compression of Large Meshes
• Slides on Crystal Dynamics

Supplementary Material

• Some Example Proofs for Homology
• Paper Treating Discrete Hodge Decompositions
• Paper Treating Boundary Sensitive Discrete Hodge Decompositions