We classify seven-dimensional nilpotent Lie groups, decomposable or of nilpotency step at most 4, endowed with left-invariant purely coclosed G(2)-structures. This is done by going through the list of all seven-dimensional nilpotent Lie algebras given by Gong, providing an example of a left-invariant 3-form phi which is a pure coclosed G(2)-structure (i.e., it satisfies d*phi=0$d*\varphi =0$, phi perpendicular to d phi=0$\varphi \wedge d\varphi =0$) for those nilpotent Lie algebras that admit them; and by showing the impossibility of having a purely coclosed G(2)-structure for the rest of them.
Purely coclosed G2-structures on nilmanifolds
Bazzoni G.;
2023-01-01
Abstract
We classify seven-dimensional nilpotent Lie groups, decomposable or of nilpotency step at most 4, endowed with left-invariant purely coclosed G(2)-structures. This is done by going through the list of all seven-dimensional nilpotent Lie algebras given by Gong, providing an example of a left-invariant 3-form phi which is a pure coclosed G(2)-structure (i.e., it satisfies d*phi=0$d*\varphi =0$, phi perpendicular to d phi=0$\varphi \wedge d\varphi =0$) for those nilpotent Lie algebras that admit them; and by showing the impossibility of having a purely coclosed G(2)-structure for the rest of them.File | Dimensione | Formato | |
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Bazzoni, Garvín, Muñoz - Purely coclosed G2‐structures on nilmanifolds.pdf
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