Quaternionic Kähler and hyperKähler manifolds with torsion and twistor spaces

Details Quaternionic Kähler and hyperKähler manifolds with torsion and twistor spaces Quaternionic Kähler and hyperKähler manifolds with torsion and twistor spaces

2001-12-15

arxiv.org/abs/math/0112157v3

J. Reine Angew. Math. 567 (2004), 215-233

Mathematics

Differential Geometry

LaTeX 17 pages, Corrections in section 6, final version to appear in Crelle's Journal

Scientific paper

The target space of a (4,0) supersymmetric two-dimensional sigma model with Wess-Zumino term has a connection with totally skew-symmetric torsion and holonomy contained in Sp(n)Sp(1) (resp. Sp(n)), QKT (resp. HKT)-spaces. We study the geometry of QKT, HKT manifold and their twistor spaces. We show that the Swann bundle of a QKT manifold admits a HKT structure with special symmetry if and only if the twistor space of the QKT manifold admits an almost hermitian structure with totally skew-symmetric Nijenhuis tensor, thus connecting two structures arising from quantum field theories and supersymmetric sigma models with Wess-Zumino term.

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