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Metric Tensor

  1. Apr 26, 2007 #1


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    This might sound a very basic question to most of you all. But could you kindly give me some information on what eactly is a Metric Tensor and what is its significance in the higher dimension study?
    (Wiki or Google info seemed too cryptic. Thus...I ask you)

    Thank You
  2. jcsd
  3. Apr 26, 2007 #2
    It allows you to calculate (short) distances or lenghts.

    If v is a (small) displacement vector,
    the length of the displacement is d² = v'.g.v
    where v' is the transpose of v,
    and g is the metric tensor,
    and "." is the multiplication.

    In coordinates notations d²=vi gij vj.

    Go to a textbook and look for the sphere in spherical coordinates,
    you will find one of the simplest metric tensor.
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