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can someone pls help me and tell me where this formular comes from:

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I know that you can derivate the curvature as the qoutient from the second and first fundamental form, does this formular comes from the theorema egregium?

Ted Shifrin
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Walter Frosch
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    No, it presumably comes from the Gauss equation(s). – Ted Shifrin Nov 19 '22 at 16:31
  • Thanks, do you have a source where I can see the details? – Walter Frosch Nov 19 '22 at 17:35
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    I’ve actually never seen this particular formula except in the case $F=0$, but you can find the Gauss equation in any standard text. See, for example, pp. 58-60 of my text, which is freely linked in my profile. – Ted Shifrin Nov 19 '22 at 18:02
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    Where did you find this formula? – Deane Nov 19 '22 at 22:46
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    It looks related to (maybe a special case?) of proposition 6.2.16 on page 285 or https://www.google.com/url?sa=t&source=web&rct=j&url=https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2018/04/analmv.pdf&ved=2ahUKEwjB55ets7v7AhUEVTUKHbuGCCkQFnoECBMQAQ&usg=AOvVaw0-AVr1GDX5Emh-g_kgANkW – Mason Nov 19 '22 at 23:37
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    @Mason This is indeed the well-known formula in the case $F=0$ to which I referred. – Ted Shifrin Nov 19 '22 at 23:49
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    To echo @Deane's question, I would need to see the material preceding this formula. Although it is close to working out correctly, it does not, as there are serious sign issues, even if I restrict to the case $F=0$. – Ted Shifrin Nov 19 '22 at 23:51
  • I refer to this post https://math.stackexchange.com/questions/748974/gaussian-curvature-k-of-of-orthogonal-parametrization-x its also an exercise in Carmo: Differential Geometry of Curves and Surfaces – Walter Frosch Dec 05 '22 at 09:12

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