# 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?

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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.

( 2018-12-04 03:58:55 -0600 )edit

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If you consider a non-symmetric "metric", you should probably define a function with a code similar to that of the method LeviCivitaConnection.coef() (starting at line 388 of src/sage/manifolds/differentiable/levi_civita_connection.py in SageMath 8.4), by replacing each instance of self._metric by your object.

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Last updated: Dec 04 '18