Coclosed G2-structures inducing nilsolitons

摘要

We show obstructions to the existence of a coclosed G 2 {mathrm{G}_{2}} -structureon a Lie algebra ?? {mathfrak{g}} of dimension seven with non-trivial center.In particular, we prove that if there exists a Lie algebra epimorphismfrom ?? {mathfrak{g}} to a six-dimensional Lie algebra ?? {mathfrak{h}} , with the kernel contained in the center of ?? {mathfrak{g}} , then any coclosed G 2 {mathrm{G}_{2}} -structure on ?? {mathfrak{g}} induces a closed and stable three form on ?? {mathfrak{h}} that defines an almost complex structure on