Revista de la Unión Matemática Argentina
versión On-line ISSN 1669-9637
BARBERIS, M. L.. A survey on hyper-Kähler with torsion geometry. Rev. Unión Mat. Argent. [online]. 2008, vol.49, n.2, pp. 121-131. ISSN 1669-9637.
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-Kähler 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.