  The geometry arising from Michelson & Strominger's study of N=4B
supersymmetric quantum mechanics with superconformal D(2,1;alpha)-symmetry is a
hyperKaehler manifold with torsion (HKT) together with a special homothety. It
is shown that different parameters alpha are related via changes in potentials
for the HKT target spaces. For alpha not 0 or -1, we describe how each such HKT
4m-manifold M is derived from a space N of dimension 4m-4 which is quaternionic
Kaehler with torsion and carries an Abelian instanton.
