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

2025/12/18 by Andrei Moroianu, Alberto Raffero, Moroianu, Andrei +3
Mathematics · #Algebraic Geometry and Number Theory #Constant (computer programming) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Heterotic string theory #Invariant (physics) #Isomorphism (crystallography) #Lie algebra #Lie group #Nilpotent #Torus #math.DG

paper · pdf · doi:10.48550/arxiv.2512.16817

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2025/12/18 · openalex created_date 2025/12/21 · openalex updated_date 2026/08/05

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

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