A survey on hyper-Kähler with torsion geometry

BARBERIS, M.L.

REVISTA DE LA UNIóN MATEMáTICA ARGENTINA

UNION MATEMATICA ARGENTINA

Lugar: Bahía Blanca; Año: 2008 vol. 49 p. 121 - 131

0041-6932

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"ahler 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.