Real and complex supersymmetric d=1 sigma models with torsions
  We derive and discuss, at both the classical and the quantum levels, generalized N = 2 supersymmetric quantum mechanical sigma models describing the motion over an arbitrary real or an arbitrary complex manifold with extra torsions. We analyze the relevant vacuum states to make explicit the fact that their number is not affected by adding the torsion terms. 
S. A. Fedoruk, E. A. Ivanov, and A. V. Smilga
hep-th math-ph math.MP