Homogeneous 4-dimensional Kaehler--Weyl Structures
Differential Geometry
2012-11-20 v1
Abstract
Any pseudo-Hermitian or para-Hermitian manifold of dimension 4 admits a unique Kaehler-Weyl structure; this structure is locally conformally Kaehler if and only if the alternating Ricci tensor vanishes. The alternating Ricci tensor takes values in a certain representation space. In this paper, we show that any algebraic possibility in this representation space can in fact be geometrically realized by a left-invariant Kaehler-Weyl structure on a 4-dimensional Lie group in either the Hermitian or the para-Hermitian setting.
Keywords
Cite
@article{arxiv.1211.4453,
title = {Homogeneous 4-dimensional Kaehler--Weyl Structures},
author = {M. Brozos-Vazquez and E. Garcia-Rio and P. Gilkey and R. Vazquez-Lorenzo},
journal= {arXiv preprint arXiv:1211.4453},
year = {2012}
}