[see also: account]
Let $F$ be as just described.
As we let $t$ vary, $f(t)$ describes a curve in $M$.
It is interesting that (1) is a necessary condition in a much larger class of functions, which we now describe.
We describe how the notion of positivity relates to the other properties.
There are quite a number of cases, but they can be described reasonably systematically.
the process described