Sp(n)U(1)-connections with parallel totally skew-symmetric torsion

2003/11/14 by Bogdan Alexandrov, Alexandrov, Bogdan
Mathematics · Physics and Astronomy · #53B05 #53B35 #53C26 #53C55 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53B05 #msc:53B35 #msc:53C26 #msc:53C55

paper · pdf · doi:10.48550/arxiv.math/0311248

24 pages; some inessential changes

openalex publication_date 2003/11/14 · arxiv created 2004/07/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the unique Hermitian connection with totally skew-symmetric torsion on a Hermitian manifold. We prove that if the torsion is parallel and the holonomy is Sp(n)U(1), considered as a subgroup of U(2n) x U(1), then the manifold is locally isomorphic to the twistor space of a quaternionic Kaehler manifold with positive scalar curvature. If the manifold is complete, then it is globally isomorphic to such a twistor space.

Citations

• A Finiteness Theorem for Quaternionic-Kaehler Manifolds with Positive Scalar Curvature

Related

• Quaternionic Kähler and hyperKähler manifolds with torsion and twistor spaces
• On nearly Kaehler geometry
• Connexions with totally skew-symmetric torsion and nearly-Kaehler geometry
• Harmonic Hermitian structures on Riemannian manifolds with skew-torsion
• \mathrm G₂-structures with parallel skew-symmetric torsion