We construct a family of compact 7-dimensional manifolds endowed with a weakly integrable generalized G2-structure with respect to a closed and non-zero 3-form. We relate the previous structures with SU(3)-structures in dimension 7. Moreover, we investigate which types of SU(3)-structures on a 6-dimensional manifold N give rise to a strongly integrable generalized G2-structure with respect to a non-zero 3-form on the product N × S1.
Generalized G_2-manifolds and SU(3)-structures
FINO, Anna Maria;
2008-01-01
Abstract
We construct a family of compact 7-dimensional manifolds endowed with a weakly integrable generalized G2-structure with respect to a closed and non-zero 3-form. We relate the previous structures with SU(3)-structures in dimension 7. Moreover, we investigate which types of SU(3)-structures on a 6-dimensional manifold N give rise to a strongly integrable generalized G2-structure with respect to a non-zero 3-form on the product N × S1.
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