Let p be a non umbilical point on a surface S in R then we have seen in a neigh bourhood of p we have a local coordinate chart U

Question

Let p be a non umbilical point on a surface S in R then we have seen in a neigh bourhood of p we have a local coordinate chart U x x on which the first and second fundamental forms can be diagonalized simultaneously I 911 da 922 da 2 II h11 dr h22 dx Please use the Cartan s structure equations to derive the following a Codazzi equation Let A11 principle curvatures then a log 911 hi and A22 922 h22 A11 and A22 are just the 02 A11 1 A22 a log

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