  A recent photometric survey in the NGC~3766 cluster led to the detection of
stars presenting an unexpected variability. They lie in a region of the
Hertzsprung-Russell (HR) diagram where no pulsation are theoretically expected,
in between the $\delta$ Scuti and slowly pulsating B (SPB) star instability
domains. Their variability periods, between $\sim$0.1--0.7~d, are outside the
expected domains of these well-known pulsators. The NCG~3766 cluster is known
to host fast rotating stars. Rotation can significantly affect the pulsation
properties of stars and alter their apparent luminosity through gravity
darkening. Therefore we inspect if the new variable stars could correspond to
fast rotating SPB stars. We carry out instability and visibility analysis of
SPB pulsation modes within the frame of the traditional approximation. The
effects of gravity darkening on typical SPB models are next studied. We find
that at the red border of the SPB instability strip, prograde sectoral (PS)
modes are preferentially excited, with periods shifted in the 0.2--0.5~d range
due to the Coriolis effect. These modes are best seen when the star is seen
equator-on. For such inclinations, low-mass SPB models can appear fainter due
to gravity darkening and as if they were located between the $\delta$~Scuti and
SPB instability strips.
