2001/11/30 by Stefan Ivanov · 2 citations
Mathematics · Physics and Astronomy · #math.DG #hep-th #msc:53C25
published as Math. Res. Lett. 11 (2004), no. 2-3, 171--186. · LaTeX, 15 pages, references added, some typos corrected, final version to appear in Math. Res. Lett
arxiv created 2004/04/26 · arxiv updated 2009/11/30
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 ()-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