Natural Almost Hermitian Structures on Conformally Foliated 4-Dimensional Lie Groups with Minimal Leaves
Let (G, g) be a 4-dimensional Riemannian Lie group with a 2-dimensional left-invariant, conformal foliation with minimal leaves. Let J be an almost Hermitian structure on G adapted to the foliation. The corresponding Lie algebra must then belong to one of 20 families according to S. Gudmundsson and M. Svensson. We classify such structures J which are almost Kähler, integrable or Kähler. Hereby, we