Aalborg Universitet

Institut for matematiske fag.

**Primary: [AP]**A. Pressley,*Elementary Differential Geometry*, 2nd ed., Springer, 2010. Tilgængelig online via online bog via AUBs Springer Link. (Husk, at adgang kræver, at du er på AAUs net, eventuelt udefra via VPN.**Secondary: [FR]**L. Fajstrup, M. Raussen, Visual Interactive Differential Geometry

No. | Date | Type | Topics | Literature | Slides etc. |
---|---|---|---|---|---|

1 | 6/9 | 2 | Curves: Regular parametrizations, tangents, speed, arc length, unit-speed parametrization | [AP], ch. 1 (apart 1.4) | |

2 | 8/9 | 1 | Curvature and torsion. Frenet-Serret formulas. | [AP], ch. 2.1-3 (apart Thm. 2.2.6, 2.3.6) | |

3 | 13/9 | 3 | Fundamental Theorem for Curves | [AP], Thm. 2.2.6, 2.3.6; [FR], ch. 1.3.5, 1.4.3 | |

4 | 15/9 | 4 | Training Session: Fundamental Theorem for Curves | as for 3 | Curves |

5 | 20/9 | 2 | Introduction to surfaces, including level set surfaces | [AP] 4.1, 4.2, 5.1 | Horias Noter -uddrag. |

6 | 22/9 | 1 | (Re-)parametrizations. Transition functions. Smooth maps | [AP] 4.2, 4.3, [FR], 2.4, 2.5 | Slides6 |

7 | 27/9 | 3 | Smooth maps between surfaces and their derivatives; (local) orientations | [AP] 4.3 - 4.5 | |

8 | 29/9 | 4 | Training Session: Smooth maps between surfaces and their derivatives | [AP] 4.3 - 4.4 | |

9 | 4/10 | 2 | First fundamental form. Isometries | [AP] 6.1 - 6.2, 6.3 (p.133), 6.4 (p. 139 - 142) | Slides9 |

10 | 6/10 | 1 | Gauss- and Weingarten map, second fundamental form, normal curvature | [AP] 7.1 - 7.2 | "movies" |

11 | 11/10 | 3 | Curvatures: normal, geodesic, Gaussian, mean, and principal | [AP] 7.3, 8.1 - 8.2 | |

12 | 13/10 | 4 | Training session: Curvature notions on surfaces | [AP] 8.1 - 8.2 | |

13 | 25/10 | 2 | Geodesic curves on a surface | [AP] 9.1 - 9.2 | |

14 | 27/10 | 1 | Geodesics are intrinsic. Theorema egregium. | [AP] 9.2.7 - 8. 10.1 - 10.2.1 | |

15 | 1/11 | 3 | Codazzi-Mainardi and Gauss equations | [AP], 10.2 | |

16 | 3/11 | 4 | Training session: Theorema Egregium | [AP], 10.2 | |

17 | 10/11 | 2 | Local Gauss-Bonnet theorem | [AP] 13.1-2 | |

18 | 6/12 | 1 | Global Gauss-Bonnet theorem | [AP] 8.6, 13.2-4 | |

19 | 8/12 | 3 | Genus and Euler characteristic of compact surfaces | [AP] 13.4 | |

20 | 16/1 | Spørgetime. 10-12. Lokale G4-102. Send spørgsmål til Lisbeth senest dagen før. | -- |

- 2 hours of lectures and 2 hours of exercises with help from the instructor
- 2 hours of lectures and 2 hours exercises; lecturer intervenes only at the end to answer questions
- 1 hour of lectures and 3 hours of reading and exercises; help from the lecturer available for around 1 hour
- No lectures. Reading, training and exercise assignments. The lecturer will not be around. Send questions to be answered next time by email.

The geometric lab.

Flotte Applets lavet af Thomas Banchoff og Steven Lovett

Visual Geometry

2d-curves Mere end 600 plane kurver og historiske facts.

3d-xplormath. Appletsmed kurver og flader.

The Geometry Center

Mathematics Archives - Topics in Mathematics - Geometry

Java En abesaddel. Thomas Banchoff.. Man kan variere funktioner etc.

JavaView - diverse flader, kurver etc.

Flatland. En novelle om at være et fladt dyr, bo i en flade (!) og udforske den fra et "indre" perspektiv.

Ikke-Euklidisk geometri Blandt andet en applet, hvori man kan udforske Poincare- og øvre halvplansmodellerne for hyperbolsk geometri.

- Normal sections on a cylinder 1
- Normal sections on a cylinder 2
- Normal sections on a hyperboloid 1
- Normal sections on a hyperboloid 2

Lisbeth Fajstrup