Natural Almost Hermitian Structures on Conformally Foliated 4-Dimensional Lie Groups with Minimal Leaves

arXiv2203.01887MaRDI QIDQ6392725

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Publication date: 3 March 2022

Abstract: Let $(G,g)$ be a 4-dimensional Riemannian Lie group with a 2-dimensional left-invariant, conformal foliation $mathcalF$ with minimal leaves. Let $J$ be an almost Hermitian structure on $G$ adapted to the foliation $mathcalF$. The corresponding Lie algebra $mathfrakg$ must then belong to one of 20 families $mathfrak{g}_1,dots,mathfrak{g}_{20}$ according to S. Gudmundsson and M. Svensson. We classify such structures $J$ which are almost K"{a}hler $(mathcalAmathcalK)$, integrable $(mathcalI)$ or K"{a}hler $(mathcalK)$. Hereby, we construct 16 multi-dimensional almost K"{a}hler families, 18 integrable families and 11 K"{a}hler families.

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