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Potential one-forms for hyperkähler structures with torsion

Liviu Ornea·Yat Sun Poon·Andrew Swann
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Abstract

It is shown that an HKT-space with closed parallel potential 1-form has $D(2,1;-1)$-symmetry. Every locally conformally hyperkähler manifold generates this type of geometry. The HKT-spaces with closed parallel potential 1-form arising in this way are characterized by their symmetries and an inhomogeneous cubic condition on their torsion.

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Liviu Ornea, Yat Sun Poon, Andrew Swann. 2002-11-27. Potential one-forms for hyperkähler structures with torsion. https://doi.org/10.1088/0264-9381%2F20%2F9%2F317

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