Purely coclosed G2‐structures on nilmanifolds

DOI10.1002/mana.202100665arXiv2111.08399OpenAlexW3214188605MaRDI QIDQ6047345

Antonio Garvín, Vicente Muñoz, Giovanni Bazzoni

Publication date: 9 October 2023

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.08399

zbMATH Keywords

nilpotent Lie groupsSU(3)-structurespurely coclosed \(\mathrm{G}_2\)-structures

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Lie algebras of Lie groups (22E60) Nilpotent and solvable Lie groups (22E25) Hodge theory in global analysis (58A14) Solvable, nilpotent (super)algebras (17B30) (G)-structures (53C10)

Cites Work

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• Nilmanifolds with a calibrated \(G_{2}\)-structure
• Riemannian manifolds with structure group \(G_ 2\)
• Cocalibrated structures on Lie algebras with a codimension one Abelian ideal
• Locally conformal parallel \(G_2\) and \(\operatorname{Spin}(7)\) manifolds
• New invariants of \(G_{2}\)-structures
• Spinorial description of \(\mathrm{SU}(3)\)- and \(\mathrm{G}_2\)-manifolds
• Curvatures of left invariant metrics on Lie groups
• On nearly parallel \(G_2\)-structures
• The geometry of three-forms in six dimensions.
• Coclosed \(\mathrm{G}_{2}\)-structures inducing nilsolitons
• Half-flat structures on products of three-dimensional Lie groups
• Purely coclosed \(\mathrm{G}_2\)-structures on 2-step nilpotent Lie groups
• The structure of underlying Lie algebras

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