Purely coclosed G₂-structures on nilmanifolds -- II

2025/10/29 by Bazzoni, Giovanni, Petracci, Giorgia
#17B30 #22E25 #53C15 #53C38 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.25511

Abstract

This paper completes the classification of seven-dimensional nilpotent Lie groups endowed with a left-invariant purely coclosed G₂-structure, initiated by the first-named author and collaborators. In this previous work, the authors provided the classification of decomposable seven-dimensional nilpotent Lie groups and of the indecomposable ones up to step 4 of nilpotency. Here, we address the case of indecomposable 5- and 6-step nilpotent Lie groups.

Citations

• A family of complex nilmanifolds with infinitely many real homotopy types

Related

• Purely coclosed G₂-structures on nilmanifolds
• Coclosed G₂-structures inducing nilsolitons
• Invariant cocalibrated G₂-structures on nilmanifolds
• The heterotic G₂-system on 2-step nilmanifolds endowed with principal torus bundles
• Torsion-free G₂₍₂₎^*-structures with full holonomy on nilmanifolds