VFD use to maintain constant flux

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When using a VFD, am I right in thinking that for an induction motor, torque available at all speeds is constant as the voltage is reduced with frequency to maintain constant flux? Also, am I right in thinking that the mechanical output power of the motor will be less when speed is reduced, as it is the product of output torque and angular vel, which of course decreases with freq?
 
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The torque is not constant over all of the speeds but it is close - for each motor, if you dig enough there is a curve detailing the V/Hz relationship - a good reference is here : http://www.yaskawa.com/site/dmdrive.nsf/(DocID)/MNEN-5JFQNV/$File/AR.MOTOR.01.pdf
 
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