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<p>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 <i>SU</i>(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 <i>SU</i>(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.</p>

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

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  • 发表日期：

    2026年3月31日

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  • Stefan Ivanov,
  • Luis Ugarte

摘要

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.