Consider a three phase reactor (inductor) using E-I or E-E laminations with phase winding on each limbs. Now inductance of R phase is given by:
Lrr: Self inductance of R-phase Mry: Mutual inductance between R and Y phase Mrb: Mutual inductance between R and B phase.
When such inductance is excited with three phase supply Mry=Mrb=-0.5*Lrr. Hence total inductance will be zero.
This means three phase reactor does not offer any inductance?