Natural almost Hermitian structures on conformally foliated 4-dimensional Lie groups with minimal leaves

Abstract

AbstractLet (G, g) be a 4-dimensional Riemannian Lie group with a 2-dimensional left-invariant, conformal foliation $$\mathcal {F}$$ F with minimal leaves. Let J be an almost Hermitian structure on G adapted to the foliation $$\mathcal {F}$$ F . We classify such structures J which are almost Kähler $$(\mathcal {A}\mathcal {K})$$ ( A K ) , integrable $$(\mathcal {I})$$ ( I ) or Kähler $$(\mathcal {K})$$ ( K ) . Hereby we construct several new multi-dimensional examples in each class.