Conformal Killing 2-forms on 4-dimensional manifolds

A. ANDRADA; M.L. BARBERIS; MOROIANU, A.

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY

SPRINGER

Lugar: Berlin; Año: 2016 vol. 50 p. 381 - 394

0232-704X

We study four-dimensional simply connected Lie groups G with a left invariantRiemannian metric g admitting non-trivial conformal Killing 2-forms. We show that eitherthe real line defined by such a form is invariant under the group action, or the metric is halfconformallyflat. In the first case, the problem reduces to the study of invariant conformallyKähler 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.