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GENERALIZED G₂-MANIFOLDS AND SU(3)-STRUCTURES

ANNA FINO

Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy

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and

ADRIANO TOMASSINI

Dipartimento di Matematica, Università di Parma, Viale G.P. Usberti 53/A, 43100 Parma, Italy

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https://doi.org/10.1142/S0129167X08005072Cited by:8 (Source: Crossref)

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.

Keywords:

AMSC: 53C10, 53C25, 83E50

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