Annals of Global Analysis and Geometry

, Volume 50, Issue 4, pp 381–394

Conformal Killing 2-forms on four-dimensional manifolds

  • Adrián Andrada
  • María Laura Barberis
  • Andrei Moroianu
Article

DOI: 10.1007/s10455-016-9517-1

Cite this article as:
Andrada, A., Barberis, M.L. & Moroianu, A. Ann Glob Anal Geom (2016) 50: 381. doi:10.1007/s10455-016-9517-1
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Abstract

We study four-dimensional simply connected Lie groups G with a left invariant Riemannian metric g admitting non-trivial conformal Killing 2-forms. We show that either the real line defined by such a form is invariant under the group action, or the metric is half-conformally flat. In the first case, the problem reduces to the study of invariant conformally Kähler structures, whereas in the second case, the Lie algebra of G belongs (up to homothety) to a finite list of families of metric Lie algebras.

Keywords

Conformal Killing forms Invariant conformally Kähler structures Half-conformally flat metrics 

Mathematics Subject Classification

53C25 53C15 53C30 

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Adrián Andrada
    • 1
  • María Laura Barberis
    • 1
  • Andrei Moroianu
    • 2
  1. 1.FAMAF-CIEM, Universidad Nacional de CórdobaCiudad UniversitariaCordobaArgentina
  2. 2.Laboratoire de Mathématiques de VersaillesUVSQ, CNRS, Université Paris-SaclayVersaillesFrance