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arXiv · 2510.05358

On a class of almost Hermitian 4-manifolds

Ethan Addison·Tedi Draghici·Mehdi Lejmi
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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.

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Ethan Addison, Tedi Draghici, Mehdi Lejmi. 2025-10-06. On a class of almost Hermitian 4-manifolds. https://arxiv.org/abs/2510.05358

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