Purely coclosed G2-structures on 2-step nilpotent Lie groups
We consider left-invariant (purely) coclosed G 2 -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 G 2 -structures. Then, we use t...
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Veröffentlicht in: | Revista matemática complutense 2022, Vol.35 (2), p.323-359 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | We consider left-invariant (purely) coclosed G
2
-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 G
2
-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 G
2
-structures is induced by one of them. Finally, we use our results to give the explicit description of the metrics induced by purely coclosed G
2
-structures on 2-step nilpotent Lie algebras with derived algebra of dimension at most two, up to automorphism. |
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ISSN: | 1139-1138 1988-2807 |
DOI: | 10.1007/s13163-021-00392-0 |