Torsion

In standard geometry, one assumes that the distance from one point to another is the same as the distance back, so that the metric tensor can be taken to be symmetric, and there is zero so-called torsion. But in for example a causal network, connections have definite directions, and there is in general no such symmetry. And if one looks at the volume of a cone this can then introduce a correction proportional to r. But as soon as there is enough uniformity to define a reasonable notion of static space, it seems that this effect must vanish. (Note that in pure mathematics there are several different uses of the word "torsion". Here I use it to refer to the antisymmetric parts of the metric tensor.)