Mathematics

Cohomogeneity one central Kähler metrics in dimension four

Document Type

Article

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. © 2023 Walter de Gruyter GmbH, Berlin/Boston.

Publication Title

Advances in Geometry

Publication Date

1-1-2023

Volume

23

Issue

3

First Page

323

Last Page

344

ISSN

1615-715X

DOI

10.1515/advgeom-2023-0011

Keywords

4-manifold, cohomogeneity one, Kähler metric

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