  The investigation of strings and M-theory involves the understanding of
various BPS solitons which in a certain approximation can be thought of as
solutions of ten- and eleven-dimensional supergravity theories. These solitons
have a brane or a intersecting brane interpretation, saturate a bound and are
associated with parallel spinors with respect to a connection of the spin
bundle of spacetime. A class of intersecting brane configurations is examined
and it is shown that the geometry of spacetime is hyper-K\"ahler with torsion.
A relation between these hyper-K\"ahler geometries with torsion and
quaternionic calibrations is also demonstrated.
