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Holonomy of the Obata connection on 2-step hypercomplex nilmanifolds
Adri\'an Andrada, Mar\'ia Laura Barberis, Beatrice Brienza
https://arxiv.org/abs/2508.07889 https://…

Holonomy of the Obata connection on 2-step hypercomplex nilmanifolds
We study the holonomy of the Obata connection on 2-step hypercomplex nilmanifolds. By explicitly computing the curvature tensor, we determine the conditions under which the Obata connection is flat, showing that this depends on the nilpotency step of each complex structure. In particular, we show that the holonomy algebra of the Obata connection is always an abelian subalgebra of $\mathfrak{sl}(n, \mathbb{H})$: to establish this, we prove the $\mathbb{H}$-solvable conjecture for 2-step hypercom…