Gauge Deformations and Embedding Theorems for Special Geometries
Differential Geometry
2010-08-02 v2
Abstract
We reduce the embedding problem for hypo SU(2) and SU(3)-structures to the embedding problem for hypo G2-structures into parallel Spin(7)-manifolds. The latter will be described in terms of gauge deformations. This description involves the intrinsic torsion of the initial G2-structure and allows us to prove that the evolution equations, for all of the above embedding problems, do not admit non-trivial longtime solutions.
Cite
@article{arxiv.0909.5549,
title = {Gauge Deformations and Embedding Theorems for Special Geometries},
author = {Sebastian Stock},
journal= {arXiv preprint arXiv:0909.5549},
year = {2010}
}
Comments
corrected Lemma 3.9, new description of SU(2)-structures in dimension five, included a section on the Cauchy-Kowalevski theorem and integral curves in Frechet spaces