How can you tell if two metrics describe the same manifold?

inquirydog_at_hotmail.com
Date: 12/08/04 

Date: 8 Dec 2004 13:32:10 -0800

Hi-

Is there an algorithm that would allow one to tell if two
different metrics describe the same manifold? Of course you can always
find a change of coordinates that transfers the first metric into the
second, but I wouldn't call that an algorithm, rather it is a more of a
hit and miss thing. Some very seemingly different metrics like

ds^2 = dx^2 - dt^2

and

ds^2 = du^2 - u^2 dv^2

both really describe the same manifold (flat Minkowskian). In this
case a simple transformation of coordinates can derive the second
metric from the first, but in general it is difficult to do this. Any
ideas?

thanks
-I

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