On a class of almost Hermitian 4-manifolds

Ethan Addison; Tedi Draghici; Mehdi Lejmi

On a class of almost Hermitian 4-manifolds

Differential Geometry 2025-10-08 v1

Authors: Ethan Addison , Tedi Draghici , Mehdi Lejmi

Abstract

Using an integral identity proved by Sekigawa \cite{Sek87} on compact almost Hermitian 4-manifolds, we naturally obtain a global characterization of the class $\mathcal{AH}_1$ of almost Hermitian 4-manifolds satisfying the first Gray curvature condition from apparently weaker conditions. Then we take steps towards a classification of almost Hermitian 4-manifolds of class $\mathcal{AH}_1$ , including proving a uniqueness result on 4-dimensional Lie algebras.

Keywords

almost Hermitian manifold Gray curvature condition integral identity classification Lie algebra

Cite

@article{arxiv.2510.05358,
  title  = {On a class of almost Hermitian 4-manifolds},
  author = {Ethan Addison and Tedi Draghici and Mehdi Lejmi},
  journal= {arXiv preprint arXiv:2510.05358},
  year   = {2025}
}

Comments

26 pages, comments are welcome

Related papers

View all related →