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

Stefan Ivanov
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Abstract

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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Stefan Ivanov. 2004-04-26. Connection with torsion, parallel spinors and geometry of Spin(7) manifolds. https://arxiv.org/abs/math/0111216

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