Results in Mathematics

, Volume 64, Issue 3, pp 357-369

First online:

Homogeneous 4-Dimensional Kähler–Weyl Structures

  • M. Brozos-VázquezAffiliated withDepartment of Mathematics, University of A Coruña
  • , E. García-RíoAffiliated withFaculty of Mathematics, University of Santiago de Compostela
  • , P. GilkeyAffiliated withMathematics Department, University of Oregon Email author 
  • , R. Vázquez-LorenzoAffiliated withFaculty of Mathematics, University of Santiago de Compostela

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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.

Mathematics Subject Classification (2010)

53A15 53C15 15A72