  We systematically include central charges into supersymmetric quantum
mechanics formulated on curved Euclidean spaces, and explain how the background
geometry manifests itself on states of the theory. In particular, we show in
detail how, from the point of view of non-relativistic d=1 world-line physics,
one can infer the existence of target space dualities typically associated with
string theory. We also explain in detail how the presence of a non-trivial
supersymmetry central charge restricts the background geometry in which a
particle may propagate.
