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Math Help - differential geometry

  1. #1
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    differential geometry

    Why a sphere is not pairwise locally isometric?
    Can someone help? Thank you.
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  2. #2
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    Quote Originally Posted by dori1123 View Post
    Why a sphere is not pairwise locally isometric?
    Can someone help? Thank you.
    Huh? A sphere can't be pairwise locally isometric all on its own. It has to be pairwise locally isometric (or not) to something else.
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  3. #3
    Super Member Rebesques's Avatar
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    I'd guess... to the plane.


    Compare their first fundamental forms, or their Gaussian curvature even.
    Last edited by Rebesques; June 9th 2009 at 08:05 AM.
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