The motor is an induction motor, NOT a brushless PM AC motor. Therefore, as an induction motor, it is compatible with the Curtis controller. It does need to be properly tuned, meaning having a number a parameters set in the Curtis. Tuning involves the use of a special handset or dongle & program. This is probably beyond you and would require you to send the motor to the Curtis dealer for the task. The handset programmer can be rented and it is possible that the dealer can "open" the controller software and instruct you how to self tune, but you should confirm that prior to purchase.
The best (easist) way is to use the controller from the original installation of the motor, or to purchase the motor and controller as a tuned package (for your application) from a reputable dealer.