Gauge Deformations and Embedding Theorems for Special Geometries

Details Gauge Deformations and Embedding Theorems for Special Geometries Gauge Deformations and Embedding Theorems for Special Geometries

2009-09-30

arxiv.org/abs/0909.5549v2

Mathematics

Differential Geometry

corrected Lemma 3.9, new description of SU(2)-structures in dimension five, included a section on the Cauchy-Kowalevski theore

Scientific paper

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.

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