SU(3)-structures on hypersurfaces of manifolds with G_2-structure

Details SU(3)-structures on hypersurfaces of manifolds with G_2-structure SU(3)-structures on hypersurfaces of manifolds with G_2-structure

2004-10-28

arxiv.org/abs/math/0410610v6

Mathematics

Differential Geometry

30 pages, v6: some minor changes of notation for a clearer exposition

Scientific paper

We study SU(3)-structures induced on orientable hypersurfaces of seven-dimensional manifolds with G_2-structure. Taking Gray-Hervella types for both structures into account, we relate the type of SU(3)-structure and the type of G_2-structure with the shape tensor of the hypersurface. Additionaly, we show how to compute the intrinsic SU(3)-torsion and the intrinsic G_2-torsion by means of exterior algebra.

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