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Math Help - Help with Umbilical Points

  1. #1
    Member kezman's Avatar
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    Help with Umbilical Points

    we need your help. We had some time trying this one:

    If P is an umbilical point then the second fundamental form is constant

    Thanks!
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  2. #2
    Super Member girdav's Avatar
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    Re: Help with Umbilical Points

    What is the link between the second fundamental form and the normal curvature?
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  3. #3
    Member kezman's Avatar
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    Re: Help with Umbilical Points

    k_n = II(X,X) and k_n is constant. But I need that II(X,Y) constant. or am I wrong?
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  4. #4
    Super Member girdav's Avatar
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    Re: Help with Umbilical Points

    Quote Originally Posted by kezman View Post
    k_n = II(X,X) and k_n is constant. But I need that II(X,Y) constant.
    Use the bi-linearity.
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  5. #5
    Member kezman's Avatar
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    Re: Help with Umbilical Points

    kn=II(X,X) =???= II(X,Y). I need something in between to reach the right side????
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