We consider left-invariant (purely) coclosed G2-structures on 7-dimensional 2-step nilpotent Lie groups. According to the dimension of the commutator subgroup, we obtain various criteria characterizing the Riemannian metrics induced by left-invariant purely coclosed G2-structures. Then, we use them to determine the isomorphism classes of 2-step nilpotent Lie algebras admitting such type of structures. As an intermediate step, we show that every metric on a 2-step nilpotent Lie algebra admitting coclosed G2-structures is induced by one of them. Finally, we use our results to give the explicit description of the metrics induced by purely coclosed G2-structures on 2-step nilpotent Lie algebras with derived algebra of dimension at most two, up to automorphism.

Purely coclosed G_2 -structures on 2-step nilpotent Lie groups

Raffero A.
2022

Abstract

We consider left-invariant (purely) coclosed G2-structures on 7-dimensional 2-step nilpotent Lie groups. According to the dimension of the commutator subgroup, we obtain various criteria characterizing the Riemannian metrics induced by left-invariant purely coclosed G2-structures. Then, we use them to determine the isomorphism classes of 2-step nilpotent Lie algebras admitting such type of structures. As an intermediate step, we show that every metric on a 2-step nilpotent Lie algebra admitting coclosed G2-structures is induced by one of them. Finally, we use our results to give the explicit description of the metrics induced by purely coclosed G2-structures on 2-step nilpotent Lie algebras with derived algebra of dimension at most two, up to automorphism.
35
2
323
359
https://arxiv.org/abs/2006.15925
2-Step nilpotent Lie algebra; G_2-Strominger system; Metric Lie algebra; Purely coclosed G_2-structure
del Barco V.; Moroianu A.; Raffero A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1786699
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