Exceptional holonomy on vector bundles with two-dimensional fibers
Differential Geometry
2013-05-14 v4
Abstract
An SU(3)- or SU(1,2)-structure on a 6-dimensional manifold N^6 can be defined as a pair of a 2-form omega and a 3-form rho. We prove that any analytic SU(3)- or SU(1,2)-structure on N^6 with d omega^2 =0 can be extended to a parallel Spin(7)- or Spin_0(3,4)-structure Phi that is defined on the trivial disc bundle N^6\times B_epsilon(0) for a sufficiently small epsilon>0. Furthermore, we show by an example that Phi is not uniquely determined by (omega,rho) and discuss if our result can be generalized to non-trivial bundles.
Cite
@article{arxiv.1010.1695,
title = {Exceptional holonomy on vector bundles with two-dimensional fibers},
author = {Frank Reidegeld},
journal= {arXiv preprint arXiv:1010.1695},
year = {2013}
}
Comments
18 pages, v2: thoroughly revised version, v3: information on financial support added, v4: further references and a remark on the final conjecture added