Cohomogeneity one central Kähler metrics in dimension four
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Thalia Jeffres
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Gideon Maschler
Abstract
A Kähler metric is called central if the determinant of its Ricci endomorphism is constant; see [12]. For the case in which this constant is zero, we study on 4-manifolds the existence of complete metrics of this type which have cohomogeneity one for three unimodular 3-dimensional Lie groups: SU(2), the group E(2) of Euclidean plane motions, 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.
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Communicated by: P. Eberlein
References
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Topology of tropical moduli spaces of weighted stable curves in higher genus
- Explicit p-harmonic functions on the real Grassmannians
- Cohomogeneity one central Kähler metrics in dimension four
- Tropical Poincaré duality spaces
- Isometries of wall-connected twin buildings
- On automorphisms of semistable G-bundles with decorations
- Abelian branched covers of rational surfaces
- Polyhedral compactifications, I
Artikel in diesem Heft
- Frontmatter
- Topology of tropical moduli spaces of weighted stable curves in higher genus
- Explicit p-harmonic functions on the real Grassmannians
- Cohomogeneity one central Kähler metrics in dimension four
- Tropical Poincaré duality spaces
- Isometries of wall-connected twin buildings
- On automorphisms of semistable G-bundles with decorations
- Abelian branched covers of rational surfaces
- Polyhedral compactifications, I
