Connection with torsion, parallel spinors and geometry of Spin(7) manifolds
摘要
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
引用
@article{arxiv.math/0111216,
title = {Connection with torsion, parallel spinors and geometry of Spin(7) manifolds},
author = {Stefan Ivanov},
journal= {arXiv preprint arXiv:math/0111216},
year = {2007}
}
备注
LaTeX, 15 pages, references added, some typos corrected, final version to appear in Math. Res. Lett