Invariant

This is also an invariant of history. Gallic disappeared because Gallic elites were quick to send their children to the Roman school. In the same way, provincial elites later taught their offspring French at the expense of the regional languages. The ruling classes are often the first to adopt the language of the invader. They do the same today with English.

Invariant virtue appears to be as mechanical as uninterrupted vice, for true excellence changes with conditions.

In an optimal language, there should be a comprehensive set of tenses, aspects, moods, and evidentials—TAME—which are all optional for use. Whether they would be expressed as verbal conjugations or particles to complement invariant verbs is a question of architectural design.

The fundamental 2-tensor also leads to a new class of invariant linear differential operators that are canonically associated to these geometries; included is a third equation studied by Gallot et al. We apply the results to study the metrisability equation, in the nullity setting described.

In the present paper this criterion is reformulated in terms of pseudotensorial invariants of the form..