https://neckpinch.com/authors/robert-ream/New arXiv papers by Robert Ream, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2010.09218/arxiv:2010.09218Fri, 16 Oct 2020 00:00:00 GMTGideon Maschler, Robert Ream — We show that integrability of an almost complex structure in complex dimension m is equivalent, in the presence of an almost hermitian metric, to m(m-1) equations involving what we call shear operators. Inspired by this, we give an ansatz for Kähler metrics in dimension m>1, for which at most m-1 of these shear equations are non-trivial. The equations for gradient Kähler-Ricci solitons in this ansatz are frame dependent PDEs, which specialize to ODEs under extra assumptions. Metrics solving the latter system include a restricted class of cohomogeneity one metrics, and we find among them complete expanding gradient Kähler-Ricci solitons under the action of the (2m-1)-dimensional Heisenberg group, and some incomplete steady solitons. We examine curvature properties and asymptotics for the former Ricci solitons. In another special case of the ansatz we present, for m=2, a class of complete metrics of a more general type which we call gradient Kähler-Ricci skew-solitons, which are cohomogeneity one under the Euclidean plane group action. This paper continues research started in [MR, AM2].Ricci solitonsKähler–Ricci solitonsKähler geometryHomogeneous spacesAnalytic minimal model program