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Connection with torsion, parallel spinors and geometry of Spin(7) manifolds

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arxiv math/0111216 v3 pith:5VBNWE7I submitted 2001-11-20 math.DG hep-th

classification math.DGhep-th
keywords spinformfundamentaltorsionconnectionlinearmanifoldsriemannian
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We show that on every Spin(7) manifold there always exists a unique linear connection with totally skew-symmetric torsion preserving a nontrivial spinor and the Spin(7) structure. We express its torsion and the Riemannian scalar curvature in terms of the fundamental 4-form. We present an explicit formula for the Riemannian covariant derivative of the fundamental 4-form in terms of its exterior differential. We show the vanishing of the (\hat)-A genus and obtain a linear relation between Betti numbers of a compact Spin(7) manifolds which are locally but not globally conformally equivalent to a space with closed fundamental 4-form. A general solution to the Killing spinor equations is presented

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the rigidity of special and exceptional geometries with torsion a closed $3$-form

    math.DG 2025-11 unverdicted novelty 7.0 of 10

    Riemannian manifolds with a closed parallel torsion 3-form are locally N × G (G semisimple), enabling simplified proofs and explicit classification of strong G2, Spin(7), and certain 8D HKT manifolds.

  2. $\mathcal{SW}$-algebras and strings with torsion

    hep-th 2024-12 conditional novelty 6.0 of 10

    For G2 and SU(3) string backgrounds with NS flux, the scalar torsion class controls the first-order deformation of the worldsheet super W-algebra couplings away from special holonomy.

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