A note on flat metric connections with antisymmetric torsion

DOI10.1016/j.difgeo.2010.01.004zbMath1201.53052arXiv0911.1602OpenAlexW2962809164WikidataQ115156379 ScholiaQ115156379MaRDI QIDQ980903

Thomas Friedrich, Ilka Agricola

Publication date: 8 July 2010

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

Full work available at URL: https://arxiv.org/abs/0911.1602

zbMATH Keywords

flat connectionskew-symmetric torsion\(G_2\)-structure

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) (G)-structures (53C10)

Related Items (14)

Tangent Lie groups are Riemannian naturally reductive spaces ⋮ Invariant affine connections on odd-dimensional spheres ⋮ Sp(3) structures on 14-dimensional manifolds ⋮ Riemannian almost CR manifolds with torsion ⋮ Bismut Ricci flat generalized metrics on compact homogeneous spaces ⋮ Generalizations of 3-Sasakian manifolds and skew torsion ⋮ Infinite families of homogeneous Bismut Ricci flat manifolds ⋮ The stability of generalized Ricci solitons ⋮ Non-Kähler Calabi-Yau geometry and pluriclosed flow ⋮ Cartan, Schouten and the search for connection ⋮ Cocalibrated G_2-manifolds with Ricci flat characteristic connection ⋮ On Bismut flat manifolds ⋮ Manifolds with vectorial torsion ⋮ Holonomy and 3-Sasakian homogeneous manifolds versus symplectic triple systems

Cites Work

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• Riemannian manifolds with structure group \(G_ 2\)
• Geometric structures of vectorial type
• On the geometry and classification of absolute parallelisms. II
• On the holonomy of connections with skew-symmetric torsion
• Parallel spinors and connections with skew-symmetric torsion in string theory.
• The existence of special orthonormal frames
• On the geometry and classification of absolute parallelisms. I
• The skew-torsion holonomy theorem and naturally reductive spaces

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