2025/09/09 by Beatrice Brienza, Udhav Fowdar, Brienza, Beatrice +5
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG
paper · pdf · doi:10.48550/arxiv.2509.07722
openalex publication_date 2025/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the holonomy of the Obata connection on Joyce hypercomplex manifolds. For all such group manifolds except SU(2n+1), we show that the holonomy group is strictly contained in the quaternionic general linear group. The case of SU(2n+1) is more subtle: for every n>1, we show that there exist infinitely many Joyce hypercomplex structures with Obata holonomy strictly contained in GL(n(n+1),ℍ). On the other hand, Soldatenkov showed that SU(3) has Obata holonomy equal to GL(2,ℍ) \citeSol, and we present here a new example on SU(5) with holonomy equal to GL(6,ℍ). Finally, we investigate Joyce hypercomplex manifolds whose restricted holonomy lie in SL(n, ℍ), yielding new compact examples of twisted Calabi-Yau manifolds.