Most 3-phase induction motors are designed to have a reasonably high locked-rotor torque (130-160%), a high breakdown torque (150-250%) and low slip (1.5-3%). A motor with a high resistance rotor has a high locked-rotor torque, but high slip and no breakdown-torque inflection point. A motor that has a low resistance rotor has low slip and high breakdown torque, but the locked rotor torque is lower than would be desirable.
A rotor bar that is close to the surface of the rotor has a low leakage reactance reactance while a rotor bar that is closer to the shaft has a higher leakage reactance. If the rotor is constructed with two rotor bars, or one elongated bar that extends toward the shaft, the effective rotor resistance is high at locked-rotor and low at the normal operating point. That happens because the rotor frequency is high at high slip and low at low slip. At locked-rotor, the rotor current is forced to flow mostly in the low-reactance part of the rotor bar near the rotor surface. The effective resistance is increased by reducing the bar area in which the current flows.
As the motor accelerates, there is a transition between high rotor-resistance characteristics and low rotor-resistance characteristics. That transition can result in an inflection in the torque vs. speed curve.
There is a Chapman text that explains and illustrates this quite well.
Here is a link.
Pull-up torque is not the name of a special or undesirable phenomenon. It is a standard part of an induction motor performance specification. The NEMA definition is:
Pull-up torque: The minimum torque developed by the motor during the period of acceleration from rest to the speed at which breakdown torque occurs. For motors which do not have a definite breakdown torque, the pull-up torque is the minimum torque developed up to rated speed. [MG 1-1.48]
For some motors, pull-up torque is equivalent to locked-rotor torque. For others, pull-up torque is less than locked-rotor torque and occurs at a speed between zero and the speed at which breakdown torque occurs. NAMA standards allow pull-up torque to be less than locked-rotor torque and, for some ratings, less than rated torque.
It is clear from the above linked reference and from similar references that rotor bar shape, position in the rotor and material are the primary factors used to shape the torque vs. speed curve of an induction motor.
Harmonic torque is generally minimized by several aspects of motor design. One factor is the selection of the number of rotor bar slots relative the the number of stator winding slots. Another is "skewing" the rotor bar slots at an angel relative to the shaft direction. A third is the distribution of the stator windings to produce a sinusoidal flux wave.
One undesirable effect of harmonic torque is a distinct dip in the torque vs. speed waveform as shown below. That is different from the relatively gentle inflection in the torque curves of some production motors.
The following figure shows the torque vs. speed curves for various double squirrel-cage rotor designs and one deep-bar rotor design. One of the deep-bar curves shows the minimum (or pull-up) torque occurring above the zero-speed (locked-rotor) torque. Note that this is a side effect of raising the stall torque, not a design that lowers the minimum torque. Thus is is not the result of poor design. The various "m" values refer to a constant that is defined to simplify the motor performance equations. The value of m = infinity indicates a motor with no double-cage or deep-bar effects.
Standard motors have sufficiently deep rotor bars to produce a curve above the m = infinity curve but a bit below the m = 2 curve. Sometimes the curve has a minimum torque inflection point below the locked-rotor torque,
Alger describes the effects of harmonic fields using a diagram similar to the above Fig. 204 from Puchstein, Lloyd, Conrad. According to Alger, an acceptable design must minimize such effects. On the other hand, a minimum torque infection point above zero speed is accepted by international motor standards.
To address a comment; "pull-up torque" is not a phenomenon it is a point on an induction motor torque vs. speed curve that is defined by international standard. If there is a minimum point on the curve that is above zero speed and above the minimum set by motor standards, the motor meets standards.