2021/07/30 by Thalia Jeffres, Jeffres, Thalia, Gideon Maschler +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG
paper · pdf · doi:10.48550/arxiv.2107.14683
arXiv admin note: text overlap with arXiv:2007.06471
arxiv created 2021/07/30 · openalex publication_date 2021/07/30 · arxiv updated 2021/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Kähler metric is called central if the determinant of its Ricci endomorphism is constant. For the case in which this constant is zero, we study on 4-manifolds the existence of complete metrics of this type which are cohomogeneity one for three unimodular 3-dimensional Lie groups: SU(2), the group of Euclidean plane motions E(2) and a quotient by a discrete subgroup of the Heisenberg group nil3. We obtain a complete classification for SU(2), and some existence results for the other two groups, in terms of specific solutions of an associated ODE system.