Potential one-forms for hyperkähler structures with torsion

Details Potential one-forms for hyperkähler structures with torsion Potential one-forms for hyperkähler structures with torsion

2002-11-27

arxiv.org/abs/math/0211427v1

Class.Quant.Grav. 20 (2003) 1845-1856

Mathematics

Differential Geometry

16 pages, Latex, no figures

Scientific paper

10.1088/0264-9381/20/9/317

It is shown that an HKT-space with closed parallel potential 1-form has
$D(2,1;-1)$-symmetry. Every locally conformally hyperk\"ahler 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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