If the arithmetic mean is:
$ \frac { \Sigma (x_i) }{n}$
and the geometric mean is
$ (\prod (1+x_i) ) ^{1/n}$
The arithmetic variance is
$ \frac { \Sigma(x_i-\mu)^2 } {n} $
then what is the geometric variance?
[I actually have an answer, while it gets a decent result I have to think about a way to check it, and it looks funny]