2022/05/09 by Alejandro Tolcachier, Tolcachier, Alejandro
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2205.04584
In this article we study the relation between flat solvmanifolds and G2-geometry. First, we give a classification of 7-dimensional flat splittable solvmanifolds using the classification of finite subgroups of GL(n,ℤ) for n=5 and n=6. Then, we look for closed, coclosed and divergence-free G2-structures compatible with the flat metric on them. In particular, we provide explicit examples of compact flat manifolds with a torsion-free G2-structure whose finite holonomy is cyclic and contained in G2, and examples of compact flat manifolds admitting a divergence-free G2-structure.