2008/11/11 by Dmitri V. Alekseevsky, Vicente Cortés, Alekseevsky, Dmitri V. +1 · 1 citation
Mathematics · Physics and Astronomy · #53A15 #53C26 #81T60 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #hep-th #math-ph #math.DG #math.MP #msc:53A15 #msc:53C26 #msc:81T60
paper · pdf · doi:10.48550/arxiv.0811.1658
arxiv created 2008/11/11 · openalex publication_date 2008/11/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give an intrinsic definition of (affine very) special real manifolds and realise any such manifold M as a domain in affine space equipped with a metric which is the Hessian of a cubic polynomial. We prove that the tangent bundle N=TM carries a canonical structure of (affine) special Kähler manifold. This gives an intrinsic description of the r-map as the map M↦ N=TM. On the physics side, this map corresponds to the dimensional reduction of rigid vector multiplets from 5 to 4 space-time dimensions. We generalise this construction to the case when M is any Hessian manifold.