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Question: Verify Bianchi Identities

Question:Verify Bianchi Identities

srikantha087 35 Maple
June 20 2015
1

As I am beginner in maple, how to verify Bianchi Identities?

For Riemannian manifold,

1) R(X, Y)*Z+R(Y, Z)*X+R(Z, X)*Y = 0 

2) ((∇)[X]R)(Y,Z)W+((∇)[Y]R)(Z,X)W+((∇)[Z]R)(X,Y)W=0

I am not getting how to define vector fields. From my previous question I understood defining vector fields particularly. From that post I tried to verify the proof, but I cant. Please tell me about how to define vector fields without taking examples.

Thank in advance.
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