Don't undervoltage an induction motor, unless you intend to create a fireball. Induction motors (95% of AC motors) speed is controlled by frequency, not voltage. To control the speed of such a motor, you need a VFD - variable frequency drive. Kicker is, there's likely a centrifugal start switch in your motor that will kick on below a certain speed, which would burn it up even if you did run it slower with a VFD.
So - you can run an AC motor slower than rated, but not with an autotransformer.
DC motor speed control can be controlled via voltage, but you would need to rectify the output of the variac to get DC anyhow.
These reasons are why most folks use either a gear drive motor or pulleys to get proper output speed.