Results in Mathematics

, Volume 64, Issue 3, pp 357–369

Homogeneous 4-Dimensional Kähler–Weyl Structures

  • M. Brozos-Vázquez
  • E. García-Río
  • P. Gilkey
  • R. Vázquez-Lorenzo
Article

DOI: 10.1007/s00025-013-0319-5

Cite this article as:
Brozos-Vázquez, M., García-Río, E., Gilkey, P. et al. Results. Math. (2013) 64: 357. doi:10.1007/s00025-013-0319-5

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 ρa vanishes. The tensor ρa 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)

53A1553C1515A72

Copyright information

© Springer Basel 2013

Authors and Affiliations

  • M. Brozos-Vázquez
    • 1
  • E. García-Río
    • 2
  • P. Gilkey
    • 3
  • R. Vázquez-Lorenzo
    • 2
  1. 1.Department of MathematicsUniversity of A CoruñaA CoruñaSpain
  2. 2.Faculty of MathematicsUniversity of Santiago de CompostelaSantiago de CompostelaSpain
  3. 3.Mathematics DepartmentUniversity of OregonEugeneUSA