A survey on hyper-K？hler with torsion geometry

manifolds with special geometric structures play a prominent role in some branches of theoretical physics, such as string theory and supergravity. for instance, it is well known that supersymmetry requires target spaces to have certain special geometric properties. in many cases these requirements can be interpreted as restrictions on the holonomy group of the target space riemannian metric. however, in some cases, they cannot be expressed in terms of the riemannian holonomy group alone and give rise to new geometries previously unknown to mathematicians. an example of this situation is provided by hyper-k？hler with torsion (or hkt) metrics, a particular class of metrics which possess a compatible connection with torsion whose holonomy lies in sp(n). a survey on recent results on hkt geometry is presented.