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From B?r: "Elementary Differential Geometry":
Sections 3.1 - 3.5, 3.7.
From Section 3.8: Ruled surfaces (pp. 132-135) and surfaces of revolution (pp. 143-145).
Sections 4.1, 4.4 - 4.7, 4.9 - 4.11.
The lecture notes Vector fields, the covariant derivative, and curvature.
Results proved in the exercises are part of the syllabus, but not the solutions.
I have added Sections 15, 16, 18, 19, 20, where the labelling refers to the new version. In Section 5 I have added the definition of the covariant derivative at a point. There are also changes in the last part of Section 17. This is the final version as far as the mathematical content is concerned, but I will correct typos and mistakes if I become aware of any.
Those students who attend the last lecture on Thursday the 23rd November will have a chance to choose a time-slot for the exam. All other students must appear at 9:00 on Wednesday the 6th December in NHA 1119 in order to be assigned a time-slot (or withdraw).
The exam will be held on 6-7 December in NHA 1119.
I have added Sections 9-11. See the link under "Teaching resources".
All students in the course are invited to participate in the course evaluation. The deadline is Thursday the 16th November.
In this new version I have added Theorem 2.2 and Corollary 2.3, which roughly correspond to pages 118-122 in the textbook.
In this new version I have added most of the material from Sections 3.5 and 3.6 of the textbook that we have covered in the lectures except Theorem 3.6.15. There are no changes to the material in the previous version except that the definitions of vector fields and normal fields have been moved to the end of Section 1.
Here is a new version of the assignment problems in which two corrections have been made:
* In Problem 2, the numbers a,b should satisfy 0<b<a (rather than 0<a<b).
* In Problem 3, the words meridian/longitude have been replaced with the expressions used in the textbook.
Here are the assignment problems. The solutions should be returned through Canvas no later than Thursday the 26th October at 14:30.
This version covers both Lie brackets, the covariant derivative, and the Riemannian curvature tensor. There are some additions in the previously published sections.
Here are notes on the Lie bracket. The notes will be expanded with material on the covariant derivative and curvature.
The student representative for this course is ?smund S?ther, asmund.olafsensather(att)fys.uio.no.
The final exam will be oral, and it will be held on the 6th and 7th December.
The assignment problems will be posted no later than the 12th October and the solutions should be returned through Canvas by the 26th October.
Here are the problems. Usually, the problems will be posted on the page "Schedule".
B?r, chapter 3: Classical surface theory.
B?r, chapter 4: The inner geometry of surfaces.
Jahren, chapter 3: Classification of surfaces.
The Gauss-Bonnet theorem, either from B?r: chapters 5 and 6, or
from notes to be written.