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arXiv · 2507.01655

Almost Calabi-Yau with torsion 6-manifolds and the instanton condition

Stefan Ivanov·Luis Ugarte
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Abstract

It is observed that on a compact almost complex Calabi-Yau with torsion (ACYT) 6-manifold with co-closed Lee form the curvature of the torsion connection is an $SU(3)$-instanton if and only if the torsion is parallel with respect to the torsion connection. The same conclusion holds for any (non necessarily compact) balanced ACYT 6-manifold. In particular, on a CYT 6-manifold the Strominger-Bismut connection is an $SU(3)$-instanton if and only if the torsion is parallel with respect to the Strominger-Bismut connection provided either the CYT 6-manifold is compact with co-closed Lee form or it is a balanced CYT 6-manifold.

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Stefan Ivanov, Luis Ugarte. 2025-07-02. Almost Calabi-Yau with torsion 6-manifolds and the instanton condition. https://arxiv.org/abs/2507.01655

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