# 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/metric.py`

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.

### Question:

**Is this possible?**

This is not my field so I'm not sure: what generalization do you need exactly? What do you want to do (in code) that you can't? A code sample (e.g. of how you wish it would work) would help.