Spin(7)-manifolds with three-torus symmetry

DOI10.1016/j.geomphys.2011.07.008zbMath1229.53060arXiv1104.3089OpenAlexW1588790601MaRDI QIDQ720682

Thomas Bruun Madsen

Publication date: 11 October 2011

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.3089

zbMATH Keywords

holonomy groupsdifferential geometric methodsgeneralized momentum mapsgeometric structutres

Mathematics Subject Classification ID

Momentum maps; symplectic reduction (53D20) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Issues of holonomy in differential geometry (53C29) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45)

Related Items

Closed forms and multi-moment maps ⋮ Cocalibrated \(\mathrm G_2\)-structures on products of four- and three-dimensional Lie groups ⋮ Hypersymplectic 4-manifolds, the \(G_2\)-Laplacian flow, and extension assuming bounded scalar curvature

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Special cohomogeneity-one metrics with \(Q^{1,1,1}\) or \(M^{1,1,0}\) as the principal orbit
• A classification of Riemannian manifolds with structure group Spin (7)
• Metrics with exceptional holonomy
• Orientable hypersurfaces of Riemannian manifolds with Spin (7) structure
• Kähler reduction of metrics with holonomy \(G_2\)
• On the construction of some complete metrics with exceptional holonomy
• Ricci-flat metrics, harmonic forms and brane resolutions
• Compact Riemannian 7-manifolds with holonomy \(G_ 2\). I
• Compact 8-manifolds with holonomy \(\text{Spin}(7)\)
• Toric \(G_{2}\) and \(\operatorname{spin}(7)\) holonomy spaces from gravitational instantons and other examples
• Nonembedding and nonextension results in special holonomy
• Sur les groupes d'holonomie homogènes de variétés à connexion affine et des variétés riemanniennes
• Deformations of G₂ and Spin(7) Structures
• Manifolds of Negative Curvature
• New complete noncompact Spin(7) manifolds
• Supersymmetric domain walls from metrics of special holonomy
• M-theory on Spin(7) manifolds