Connexions with totally skew-symmetric torsion and nearly-Kaehler geometry

2007/09/08 by Paul-Andi Nagy, Nagy, Paul-Andi
Mathematics · Physics and Astronomy · #53C12 #53C24 #53C55 #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Quantum Mechanics and Non-Hermitian Physics #math.DG #msc:53C12 #msc:53C24 #msc:53C55

paper · pdf · doi:10.48550/arxiv.0709.1231

45 pages

arxiv created 2007/09/08 · openalex publication_date 2007/09/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study almost Hermitian structures admitting a Hermitian connexion with totally skew-symmetric torsion or equivalently, those almost Hermitian structures with totally skew-symmetric Nijenhuis tensor. We investigate up to what extent the Nijenhuis tensor fails to be parallel with respect to the characteristic connexion. This is naturally described by means of an extension of the notion of Killing form to almost Hermitian geometry. In this context, we also make an essentially self-contained survey of nearly-Kaehler geometry, but from the perspective of non-integrable holonomy systems.

Related

• Torsion in almost Kaehler geometry
• Algebraic reduction of certain almost Kaehler manifolds
• Sp(n)U(1)-connections with parallel totally skew-symmetric torsion
• The Srni lectures on non-integrable geometries with torsion
• On nearly Kaehler geometry