October 13, 2025Open Access

Parallel torsion and G₂, Spin (7) instantons

Key Points

The curvature of the characteristic connection is a G2 instanton when the torsion 3-form is parallel.
On compact Spin(7) manifolds, the torsion connection is a Spin(7) instanton if the torsion 3-form is closed.
An integrable G2 manifold exhibits a unique connection with respect to its Lee form and instanton conditions.
The study highlights the deep interconnection between torsion forms and instanton properties across different manifolds.

Abstract

Instanton properties of the characteristic connection on an integrable G₂ manifold as well as instanton condition of the torsion connection on a Spin (7) manifold are investigated. It is shown that for an integrable G₂ manifold with -parallel Lee form the curvature of the characteristic connection is a G₂ instanton exactly when the torsion 3-form is -parallel. It is observed that on a compact Spin (7) manifold with closed torsion 3-form the torsion connection is a Spin (7) instanton if and only if the torsion 3-form is parallel with respect to the torsion connection.

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