Metric Tensor

  • Thread starter rbt
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  • #1
rbt
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Hi,

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
 

Answers and Replies

  • #2
1,227
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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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