# Differential Geometry III

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.

### (19205201)

active participation: at least 60% requested, regular participation: at least 85% requestedType | Lecture |
---|---|

Instructor | Prof. Dr. Konrad Polthier, Henriette Lipschütz |

Language | English |

Start | Oct 17, 2018 | 12:00 PM |

end | Feb 13, 2019 | 02:00 PM |

Time | * Lecture: Wednesday, 12:15 - 13:45, SR 140/A7 (starting Oct., 17th, 2018) * Tutorials (starting Oct., 26th, 2018):
* Oral exams: Feb., 14th, 2019, 11:00 - 12:00. |

## Requirements

Differential geometry I

## Literature

- Lee, John M., Introduction to Smooth Manifolds, Springer, 2012
- Lee, John M., Riemannian Manifolds: An Introduction to Curvature, Springer, 1997
- Kühnel, Wolfgang, Differentialgeometrie:Kurven - Flächen - Mannigfaltigkeiten, Springer, 2012
- O'Neill, Barret: Semi-Riemannian Geometry with Applications to Relativity, Academic Press, 1983
- Guillemin, Victor and Pollack, Alan: Differential Topology, AMS Chelsea Publishing, 2010
- Hirsch, Morris: Differential Topology, Graduate Texts in Mathematics, Springer, 1997
- Kreck, Matthias: Differential Algebraic Topology, Graduate Studies in Mathematics, Band 110, AMS, 2010
- Munkres, James: Topology, Pearson New International Edition, 2013

Further Reading:

- Minimum number of charts for RP^n: http://link.springer.com/chapter/10.1007%2FBFb0085228
- Foundations of Geometric Algebra Computing: https://www.springer.com/de/book/9783642317934
- Subdivision Surfaces: https://www.springer.com/de/book/9783540764052
- Generalized Curvatures: https://www.springer.com/de/book/9783540737919
- Computational Conformal Geometry: https://books.google.de/books/about/Computational_Conformal_Geometry.html?id=4FDvAAAAMAAJ&source=kp_cover&redir_esc=y
- Variational Principles for Discrete Surfaces: https://books.google.de/books?id=hVvvAAAAMAAJ&source=gbs_similarbooks
- Ricci Flow for Shape Analysis and Surface Registration:https://books.google.de/books?id=E-u3BAAAQBAJ&source=gbs_similarbooks
- Polygon Mesh Processing: http://www.pmp-book.org/