sadegh4137
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consider we have n dimensional manifold,N
at point p we can define a vector
this vector is independent of our coordinate.
assume we choose two chart (u,ψ) and (v,Ω) that intersection of ψ and Ω is not empty.
in this situation, we know a vector define at p in chart (u,ψ) transforms to chart (v,Ω) with this relation
[itex]v^μ{}[/itex]=[itex]\frac{}4{}21[/itex]
at point p we can define a vector
this vector is independent of our coordinate.
assume we choose two chart (u,ψ) and (v,Ω) that intersection of ψ and Ω is not empty.
in this situation, we know a vector define at p in chart (u,ψ) transforms to chart (v,Ω) with this relation
[itex]v^μ{}[/itex]=[itex]\frac{}4{}21[/itex]
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