Cohomogeneity one central Kähler metrics in dimension four
Jeffres, Thalia D.
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Jeffres, T., Maschler, G., & Ream, R. (2023). "Cohomogeneity one central Kähler metrics in dimension four." Advances in Geometry, 23(3), (pp. 323-344). https://doi.org/10.1515/advgeom-2023-0011
A Kähler metric is called central if the determinant of its Ricci endomorphism is constant; see . 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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