Work

Parallel torsion and $$G_2, Spin(7)$$ instantons

Year: 2026

Type: article

Abstract: Instanton properties of the characteristic connection $${\nabla }$$ ∇ on an integrable $$G_2$$ G 2 manifold as well as instanton condition of the torsion connection $${\nabla }$$ ∇ on a Spin (7) manifold are investigated. It is shown that for an integrable $$G_2$$ G 2 manifold with $${\nabla }$$ ∇ -parallel Lee form the curvature of the characteristic connection is a $$G_2$$ G 2 instanton exactly when the torsion 3-form is $${\nabla }$$ ∇ -parallel. It is observed that on a compact Spin (7) manifold with $${\nabla }$$ ∇ 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.

Source: Revista Matemática Complutense

DOI: 10.1007/s13163-026-00580-w

Authors: Stefan Ivanov, Alexander Petkov, Luis Ugarte

Institutions: Bulgarian Academy of Sciences, Institute of Mathematics and Informatics, Sofia University "St. Kliment Ohridski", Universidad de Zaragoza

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Ministerio de Ciencia, Innovación y Universidades, Bulgarian National Science Fund