Differential Geometry I - Dietmar Salamon - 2017

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22.1.2018 09:30-10:00 Nicholas

The mighty Salamon will most likely manage to intimidate you at several points during the exam. But fear not, he can also smile, it just depends on what you’re saying. The exam is on the blackboard, with Salamon and some assistant sitting at the table.

He starts out with examples, something which I indeed didn’t really study. Thankfully, it was: give me a motion with pure sliding, this is fairly simple. He then wanted me to give the Phi too, at which point I started failing, and in response, Salamon looked as though he might yell at me or hit me. He did not.

Next, I had to explain when two manifolds with const sect curv k are isometric, with proof, and unlike the script, it is not enough to simply say “global CAH and csc theorem”.

Now the exam started to go really well, I got to talk about the exponential map, Hopf Rinow, which lemmata are used, prove curve shortening lemma. At this point he is smiling rather than looking angry.

Then he asks me what I want to talk about, so I prove the isometries theorem, with mostly oral explanations and writing down the key formulas, and the diagram.

Lastly, he wants to know why the exponential map is smooth. This follows from Picard Lindelöf, geodesics are integral curves of the geodesic spray.

That was it, the exam ended two or three minutes early, and started without delay.