1997/10/08 by P. S. Howe, Paul Howe, A. Opfermann +1 · 52 citations
Engineering · Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Engineering #Geometry and complex manifolds #Kähler manifold #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Pure mathematics #Supergravity #Supersymmetry #Torsion (gastropod) #Twistor space #Twistor theory #dg-ga #gr-qc #hep-th #math.DG
paper · pdf · doi:10.1007/s002200050469
published in Communications in Mathematical Physics 197(3), 713-727 (Springer Science+Business Media) · 25 pages, phyzzx
arxiv created 1997/10/08 · openalex publication_date 1998/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We find that the target space of two-dimensional (4,0) supersymmetric sigma models with torsion coupled to (4,0) supergravity is a QKT manifold, that is, a quaternionic Kähler manifold with torsion. We give four examples of geodesically complete QKT manifolds one of which is a generalisation of the LeBrun geometry. We then construct the twistor space associated with a QKT manifold and show that under certain conditions it is a Kähler manifold with a complex contact structure. We also show that, for every 4k-dimensional QKT manifold, there is an associated 4(k+1)-dimensional hyper-Kähler one.