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Nov 14, 2012 at 17:35 vote accept Matthias Plaue
Nov 14, 2012 at 17:35
Oct 26, 2012 at 15:34 history edited Ian Agol CC BY-SA 3.0
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Oct 26, 2012 at 2:33 comment added Ian Agol @GB: it's not trivial. I'll try to give a more detailed argument later using 2nd variation. But notice the 2nd fund. form depends only on the 2nd derivative at a point. If two surfaces agree to 2nd order, then so will the time t evolute. So the curvature depends only on the 2nd fund. form.
Oct 25, 2012 at 21:47 comment added J. GE @Agol "This is because under the orthogonal flow for time t, the second fundamental form at time t is determined uniquely by the second fundamental form at time 0." Is this statement trivial?
Oct 25, 2012 at 21:28 history edited Ian Agol CC BY-SA 3.0
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Oct 24, 2012 at 17:21 history answered Ian Agol CC BY-SA 3.0