Curvature of almost quaternion-Hermitian manifolds

2007/08/02 by Francisco Martı́n Cabrera, Francisco Martin Cabrera, Andrew Swann +2
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C10 #msc:53C15 #msc:53C55

paper · pdf · doi:10.48550/arxiv.0708.0309

40 pages

arxiv created 2007/08/02 · arxiv updated 2009/12/01

Abstract

We study the decomposition of the Riemannian curvature R tensor of an almost quaternion-Hermitian manifold under the action of its structure group Sp(n)Sp(1). Using the minimal connection, we show that most components are determined by the intrinsic torsion ξand its covariant derivative \widetilde∇ξand determine relations between the decompositions of ξ⊗ξ, \widetilde∇ξand R. We pay particular attention to the behaviour of the Ricci curvature and the q-Ricci curvature.

Related

• Curvature of (special) almost Hermitian manifolds
• Almost Quaternion-Hermitian Manifolds
• Curvature of quaternionic skew-Hermitian manifolds and bundle constructions
• The intrinsic torsion of almost quaternion-Hermitian manifolds
• Curvature of almost Hermitian manifolds and applications