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

Emma Andersdotter Svensson; Sigmundur Gudmundsson

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

Differential Geometry 2022-01-12 v1

Authors: Emma Andersdotter Svensson , Sigmundur Gudmundsson

Abstract

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

Keywords

riemannian lie groups conformal foliations minimal leaves almost hermitian structures almost kähler kähler 4-dimensional

Cite

@article{arxiv.2201.03854,
  title  = {Natural almost Hermitian structures on conformally foliated 4-dimensional Lie groups with minimal leaves},
  author = {Emma Andersdotter Svensson and Sigmundur Gudmundsson},
  journal= {arXiv preprint arXiv:2201.03854},
  year   = {2022}
}

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