Geometry of Hyper-Kähler Connections with Torsion

1999/08/03 by Gueo Grantcharov, Yat Sun Poon · 7 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Combinatorics #Connection (principal bundle) #Geometry #Geometry and complex manifolds #Hermitian matrix #Holomorphic function #Holonomy #Homogeneous #Mathematical analysis #Mathematical physics #Mathematics #Pure mathematics #Torsion (gastropod) #hep-th #math-ph #math.DG #math.MP

paper · pdf · doi:10.1007/s002200000231

published as Commun.Math.Phys. 213 (2000) 19-37 · 21 pages, LaTeX

arxiv created 1999/08/03 · openalex publication_date 2000/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The internal space of a N=4 supersymmetric model with Wess-Zumino term has a connection with totally skew-symmetric torsion and holonomy in \SP(n). We study the mathematical background of this type of connections. In particular, we relate it to classical Hermitian geometry construct homogeneous as well as inhomogeneous examples, characterize it in terms of holomorphic data, develop its potential theory and reduction theory.

Citations

• Twistor spaces for hyper-Kähler manifolds with torsion
• Complex structures on nilpotent Lie algebras

Cited by

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• Subvarieties of hypercomplex manifolds with holonomy in SL(n,H)
• The spinorial geometry of supersymmetric heterotic string backgrounds
• Geometry of quaternionic Kähler connections with torsion
• Abelian Hermitian geometry
• Bi-HKT and bi-Kähler supersymmetric sigma models