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