Completeness of projective special K "ahler and quaternionic K "ahler\n manifolds

2016/07/25 by Vicente Cortés, Cortés, Vicente, Malte Dyckmanns +3
Mathematics · #53C26 #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)

paper · pdf · doi:10.48550/arxiv.1607.07232

openalex publication_date 2016/07/25 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We prove that every projective special K "ahler manifold with \regular\nboundary behaviour is complete and defines a family of complete quaternionic\nK "ahler manifolds depending on a parameter c\≥ 0. We also show that,\nirrespective of its boundary behaviour, every complete projective special\nK "ahler manifold with \cubic prepotential gives rise to such a family.\nExamples include non-trivial deformations of non-compact symmetric quaternionic\nK "ahler manifolds.\n

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