, Volume 64, Issue 3-4, pp 357-369
Date: 26 May 2013

Homogeneous 4-Dimensional Kähler–Weyl Structures

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Abstract

Any pseudo-Hermitian or para-Hermitian manifold of dimension 4 admits a unique Kähler–Weyl structure; this structure is locally conformally Kähler if and only if the alternating Ricci tensor ρ a vanishes. The tensor ρ a takes values in a certain representation space. In this paper, we show that any algebraic possibility Ξ in this representation space can in fact be geometrically realized by a left-invariant Kähler–Weyl structure on a 4-dimensional Lie group in either the Hermitian or the para-Hermitian setting.