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arXiv · 2304.04284

G$_2$-instantons on $2$-step nilpotent Lie groups

Andrew Clarke·Viviana del Barco·Andrés J. Moreno
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Abstract

We study the G$_2$-instanton condition for a family of metric connections arisen from the characteristic connection, on $7$-dimensional $2$-step nilpotent Lie groups with left-invariant coclosed G$_2$-structures. According to the dimension of the commutator subgroup, we establish necessary and sufficient conditions for the connection to be an instanton, in terms of the torsion of the G$_2$-structure, the torsion of the connection and the Lie group structure.Moreover, we show that in our setup, G$_2$-instantons define a naturally reductive structure on the simply connected $2$-step nilpotent Lie group with left-invariant Riemannian metric. Taking quotient by lattices, one obtains G$_2$-instantons on compact nilmanifolds.

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Andrew Clarke, Viviana del Barco, Andrés J. Moreno. 2023-04-09. G$_2$-instantons on $2$-step nilpotent Lie groups. https://arxiv.org/abs/2304.04284

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