2010/09/14 by Luis Carlos de Andrés, Luis C. de Andrés, Marisa Fernández +10
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG
paper · pdf · doi:10.48550/arxiv.1009.2745
This paper is an expanded version of sections 1,2,3,4,5 and 6 of arXiv:0903.1398
arxiv created 2010/09/14 · openalex publication_date 2010/09/14 · arxiv updated 2010/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct left invariant quaternionic contact (qc) structures on Lie groups with zero and non-zero torsion and with non-vanishing quaternionic contact conformal curvature tensor, thus showing the existence of non-flat quaternionic contact manifolds. We prove that the product of the real line with a seven dimensional manifold, equipped with a certain qc structure, has a quaternionic Kaehler metric as well as a metric with holonomy contained in Spin(7). As a consequence we determine explicit quaternionic Kaehler metrics and Spin(7)-holonomy metrics which seem to be new. Moreover, we give explicit non-compact eight dimensional almost quaternion hermitian manifolds with either a closed fundamental four form or fundamental two forms defining a differential ideal that are not quaternionic Kaehler.