%0 Journal Article
%T Homogeneous 4-dimensional Kaehler--Weyl Structures
%A M. Brozos-Vazquez
%A E. Garcia-Rio
%A P. Gilkey
%A R. Vazquez-Lorenzo
%J Mathematics
%D 2012
%I arXiv
%X 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.
%U http://arxiv.org/abs/1211.4453v1