- #1
AlephClo
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Q1: How do we prove that a Riemannian metric G (ex. on RxR) is invariant with respect to a change of coordinate, if all we have is G, and no coordinate transform?
G = ( x2 -x1 )
( -x1 x2 )
Q2: Since the distance ds has to be invariant, I understand that it has to be proved independantly of a specific coordinate transform. Any relationships between a given Riemannian metric and coordinate transforms?
Thank you
G = ( x2 -x1 )
( -x1 x2 )
Q2: Since the distance ds has to be invariant, I understand that it has to be proved independantly of a specific coordinate transform. Any relationships between a given Riemannian metric and coordinate transforms?
Thank you
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