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Sagemanifold - Connection components from a tensor (not a metric)

Dear community.

This might sound dump, but I'm trying to determine whether a tensor satisfy the properties of a metric (under certain conditions). Of course it is a (0,2)-symmetric tensor, call it $S$, but I cannot (to my understanding) calculate the (Levi-Civita-like) connection components that would be associated to $S$... unless I declare it as a metric.

The way it is implemented makes sense... and it's solid!

What I did...?

I defined like a metric and calculate the associated connection (and curvatures)

Why should I do something else?

In the file src/sage/manifolds/differentiable/ the metric is defined (as it should) to be symmetric, but it does not allow to consider extensions of General Relativity like say Einstein--Strauss model. Thus, I need an instance to calculate the derived quantities of a tensor that is a generalization of a metric.


Is this possible?