Holomorphic harmonic morphisms from four-dimensional non-Einstein manifolds
Differential Geometry
2014-05-22 v2
Abstract
We construct 4-dimensional Riemannian Lie groups carrying left-invariant conformal foliations with minimal leaves of codimension 2. We show that these foliations are holomorphic with respect to an (integrable) Hermitian structure which is not K\" ahler. We then prove that the Riemannian Lie groups constructed are {\it not} Einstein manifolds. This answers an important open question in the theory of complex-valued harmonic morphisms from Riemannian 4-manifolds.
Keywords
Cite
@article{arxiv.1405.5053,
title = {Holomorphic harmonic morphisms from four-dimensional non-Einstein manifolds},
author = {Sigmundur Gudmundsson},
journal= {arXiv preprint arXiv:1405.5053},
year = {2014}
}
Comments
Keywords: harmonic morphisms, holomorphic, Einstein manifolds. arXiv admin note: substantial text overlap with arXiv:1310.5113, arXiv:1312.2783