Geometrical CP violation in the N-Higgs-doublet model

Geometrical CP violation is a particular type of spontaneous CP violation
in which the vacuum expectation values have phases which are calculable,
i.e. stable against the variation
of the free parameters of the scalar potential.
Although originally suggested
within a specific version of the three-Higgs-doublet model,
it is a generic phenomenon.
We investigate its viability and characteristic features
in models with several Higgs doublets.
Our work contains both general results and illustrative examples.