  Context: B[e] supergiants are known to have non-spherical winds, and the
existence of disks that are neutral in hydrogen close to their stellar surface
has been postulated. A suitable mechanism to produce non-spherical winds seems
to be rapid rotation, and at least for three B[e] supergiants in the Magellanic
Clouds rotation velocities at a substantial fraction of their critical velocity
have been found. Aims: We want to find suitable recombination distances in the
equatorial plane of rapidly rotating stars that explain the observed huge
amounts of neutral material in the vicinity of B[e] supergiants. Methods: We
perform ionization structure calculations in the equatorial plane around
rapidly rotating luminous supergiants. The restriction to the equatorial plane
allows us to treat the ionization balance equations 1-dimensionally, while the
stellar radiation field is calculated 2-dimensionally, taking into account the
latitudinal variation of the stellar surface parameters. The stellar parameters
used correspond to those known for B[e] supergiants. The assumptions made in
the computations all have in common that the total number of available ionizing
photons at any location within the equatorial plane is overestimated, resulting
in upper limits for the recombination distances. Results: We find that despite
the drop in equatorial surface density of rapidly rotating stars (neglecting
effects like bi-stability and/or wind compression), hydrogen and helium
recombine at or close to the stellar surface, for mass loss rates Mdot > 5d-5
M_sun/yr and rotation speeds in excess of v(rot,eq)/v(crit)=0.8.
