Harmonic \(\operatorname{G}_2\)-structures on almost abelian Lie groups

DOI10.1016/j.difgeo.2023.102060arXiv2212.05168OpenAlexW4386843970MaRDI QIDQ6123235

Andrés J. Moreno

Publication date: 4 March 2024

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2212.05168

zbMATH Keywords

almost abelian Lie groups\(\operatorname{G}_2\)-structures

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Nilpotent and solvable Lie groups (22E25) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15)

Cites Work

• Unnamed Item
• Unnamed Item
• The Ricci flow in a class of solvmanifolds
• Soliton solutions for the Laplacian co-flow of some \(G_2\)-structures with symmetry
• \(G_2\)-manifolds and associative submanifolds via semi-Fano 3-folds
• Riemannian manifolds with structure group \(G_ 2\)
• Cocalibrated structures on Lie algebras with a codimension one Abelian ideal
• The Ricci tensor of SU(3)-manifolds
• Calibrated geometries
• Structure of homogeneous Riemann spaces with zero Ricci curvature
• Curvatures of left invariant metrics on Lie groups
• Lattices in almost abelian Lie groups with locally conformal Kähler or symplectic structures
• The Laplacian coflow on almost-abelian Lie groups
• On the construction of some complete metrics with exceptional holonomy
• Compact Riemannian 7-manifolds with holonomy \(G_ 2\). I
• Weyl-Einstein structures on conformal solvmanifolds
• Harmonic \(\text{Sp}(2)\)-invariant \(\text{G}_2\)-structures on the 7-sphere
• A new construction of compact torsion-free \(G_2\)-manifolds by gluing families of Eguchi-Hanson spaces
• Estimates and Monotonicity for a heat flow of isometric \(G_2\)-structures
• Balanced Hermitian structures on almost abelian Lie algebras
• Harmonic G-structures
• FLOWS OF G2-STRUCTURES, I
• Classification of G ₂ -Structures
• Closed warped G_2-structures evolving under the Laplacian flow
• Laplacian flow of homogeneous G2-structures and its solitons
• Extremally Ricci pinched \(G_2\)-structures on Lie groups

This page was built for publication: Harmonic \(\operatorname{G}_2\)-structures on almost abelian Lie groups