The heterotic G₂-system on 2-step nilmanifolds endowed with principal torus bundles

2025/12/18 by Andrei Moroianu, Alberto Raffero, Moroianu, Andrei +3
#math.DG

paper · pdf · doi:10.48550/arxiv.2512.16817

Abstract

We study the geometric heterotic G₂-system on 7-dimensional 2-step nilmanifolds M=Γ\backslash N endowed with principal torus bundles and with a prescribed flat tangent bundle instanton. We first prove that every invariant G₂-structure solving the system must be coclosed when the dimension of the commutator of N is 1 or 2, and under an additional calibration assumption when the dimension is 3. Then, we discuss the existence of solutions for all possible isomorphism classes of 7-dimensional 2-step nilpotent Lie algebras, and we provide examples with constant dilaton function.

Citations

• Curvatures of left invariant metrics on lie groups
• On the Cohomology of Compact Homogeneous Spaces of Nilpotent Lie Groups

Related

• Purely coclosed G₂-structures on nilmanifolds -- II
• Purely coclosed G₂-structures on nilmanifolds
• Invariant cocalibrated G₂-structures on nilmanifolds
• Torsion-free G₂₍₂₎^*-structures with full holonomy on nilmanifolds
• G₂-instantons on 2-step nilpotent Lie groups