Almost Hermitian Structures on Conformally Foliated Lie Groups

Seminar in Mathematical Modelling and Analysis

Abstract: I will present my master’s thesis as well as give a brief introduction to Riemannian geometry. In the thesis, we let (G, g) be a 4-dimensional Riemannian Lie group with a 2-dimensional left-invariant, conformal foliation F with minimal leaves and adapt an almost Hermitian structure J on G to the foliation F. In 2014, S. Gudmundsson and M. Svensson showed that the corresponding Lie algebra of G must then belong to one of 20 families. In the thesis, we classify such structures J which are almost Kähler (AK), integrable (I) or Kähler (K). Hereby, we construct 16 multi-dimensional almost Kähler families, 18 integrable families and 11 Kähler families.