Avoid covariant indices in the Levi-Civita Tensor

[Alejandro Guarnizo Trilleras]

Hi all,

I'm start learning xact and trying to make long contractions of vector fields with metrics and Levi-Civita tensors.

My manifold is defined as 

DefMetric[-1, gb[-a, -b], CD, SymbolOfCovD -> {"D", "⌡"}]

valueEta = {{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}};

AllComponentValues[gb[{a, cartesian}, {b, cartesian}], valueEta];

After all I just simply defined a vector field as

DefTensor[A[μ], M4]

and I tried to make all possible contractions as

epsilongb[μ, ν, α, β] gb[ρ, σ] gb[γ, δ]A[-μ] A[-ν] (CD[-α][A[-β]]) (CD[-ρ][A[-σ]]) (CD[-γ][A[-δ]] //ContractMetric // PutScalar // Simplification // FullSimplify

The "problem" is that I obtained results as

There is any way to"force" xact to have all indices contravariant?. I appreciate your kind support.