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Question: Riemannian Connection,Metric Tensor

I am beginner in maple. And my field is Differential geometry. I am trying this calculation through maple.

I have these vector fields e1=z2D_x,e2=z2D_y,e3=z2D_z

Now I have to calculate 2g(e1e3,e1) using maple. where The Riemannian connection  of the metric tensor g is given by Koszul's formula

2g(XY,Z)=Xg(Y,Z)+Yg(Z,X)Zg(X,Y)g(X,[Y,Z])g(Y,[X,Z])+g(Z,[X,Y])

By calculated manually I got 2g(e1e3,e1)=2g(−(2/z) e1,e1)

So help me in simplifying tedious calculations using maple. I will try to learn.

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