Examples of hyper-Kähler connections with torsion (Q2715750)

On a hyper-Hermitian manifold there are two natural torsion-free connections, namely the Levi-Civita connection and the Obata connection. However, in general the Levi-Civita connection does not preserve the hypercomplex structure and the Obata connection does not preserve the metric. A linear connection \(\nabla\) on a hyper-Hermitian manifold is hyper-Hermitian if \(\nabla g=0\) and \(\nabla I_1=\nabla I_2=\nabla I_3\), where \(I_1, I_2,I_3\) form the hypercomplex structure. Note that a general hyper-Hermitian connection has torsion. In this paper the author presents some examples of HKT-connections (hyper-Kähler with torsion). A holomorphic characterization of HKT-structure is also given.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00032].