Purely coclosed G2‐structures on nilmanifolds

Giovanni Bazzoni, Antonio Garvín and Vicente Muñoz

Mathematische Nachrichten, 2023, vol. 296, issue 6, 2236-2257

Abstract: We classify seven‐dimensional nilpotent Lie groups, decomposable or of nilpotency step at most 4, endowed with left‐invariant purely coclosed G2‐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 φ which is a pure coclosed G2‐structure (i.e., it satisfies d∗φ=0$d*\varphi =0$, φ∧dφ=0$\varphi \wedge d\varphi =0$) for those nilpotent Lie algebras that admit them; and by showing the impossibility of having a purely coclosed G2‐structure for the rest of them.

Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.202100665

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:296:y:2023:i:6:p:2236-2257

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().