3-Sasakian manifolds in dimension seven, their spinors and G\(_2\)-structures

DOI10.1016/j.geomphys.2009.10.003zbMath1188.53041arXiv0812.1651OpenAlexW2028890444WikidataQ115156378 ScholiaQ115156378MaRDI QIDQ2266917

Ilka Agricola, Thomas Friedrich

Publication date: 26 February 2010

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

Full work available at URL: https://arxiv.org/abs/0812.1651

zbMATH Keywords

Killing spinorsconnection with torsion3-Sasakian manifoldcalibrated \(G_2\)-manifold

Mathematics Subject Classification ID

String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Almost contact and almost symplectic manifolds (53D15)

Related Items (28)

Invariant affine connections on odd-dimensional spheres ⋮ Quaternionic Heisenberg groups as naturally reductive homogeneous spaces ⋮ Eigenvalue estimates for Dirac operators in geometries with torsion ⋮ Spinors of real type as polyforms and the generalized Killing equation ⋮ Invariant connections and \(\nabla\)-Einstein structures on isotropy irreducible spaces ⋮ Odd‐dimensional counterparts of abelian complex and hypercomplex structures ⋮ The second Dirac eigenvalue of a nearly parallel \(G_{2}\)-manifold ⋮ Generalized Killing spinors on spheres ⋮ Spinorial description of \(\mathrm{SU}(3)\)- and \(\mathrm{G}_2\)-manifolds ⋮ Sasakian quiver gauge theories and instantons on cones over round and squashed seven-spheres ⋮ Structure theory of naturally reductive spaces ⋮ Invariant spinors on homogeneous spheres ⋮ Generalizations of 3-Sasakian manifolds and skew torsion ⋮ Compactifications of indefinite 3-Sasaki structures and their quaternionic Kähler quotients ⋮ Homogeneous Sasakian and 3-Sasakian structures from the spinorial viewpoint ⋮ Geometric flows of \(\mathrm{G}_2\)-structures on 3-Sasakian 7-manifolds ⋮ Quaternionic Kähler and \(\mathrm{Spin}(7)\) metrics arising from quaternionic contact Einstein structures ⋮ Jacobi relations on naturally reductive spaces ⋮ Almost contact metric structures induced by $G_2$ structures ⋮ Gauge theory and \(\mathrm{G}_2\)-geometry on Calabi-Yau links ⋮ Generalized Killing spinors on Einstein manifolds ⋮ On the curvature properties of manifolds with deformed \(G_2\) structures ⋮ Affine connections on 3-Sasakian homogeneous manifolds ⋮ Einstein locally conformal calibrated \(G_2\)-structures ⋮ Instantons and Killing spinors ⋮ Some remarks on Calabi-Yau and hyper-Kähler foliations ⋮ Cones of \(G\) manifolds and Killing spinors with skew torsion ⋮ Killing and twistor spinors with torsion

Cites Work

• Riemannian manifolds with structure group \(G_ 2\)
• 7-dimensional compact Riemannian manifolds with Killing spinors
• On nearly parallel \(G_2\)-structures
• Killing spinor equations in dimension 7 and geometry of integrable \(G_{2}\)-manifolds
• On the holonomy of connections with skew-symmetric torsion
• The Casimir operator of a metric connection with skew-symmetric torsion
• Parallel spinors and connections with skew-symmetric torsion in string theory.
• \(G_2\)-manifolds with parallel characteristic torsion
• A brief note on the spectrum of the basic Dirac operator
• Der erste Eigenwert des Dirac‐Operators einer kompakten, Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung
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