On generalized $G_2$-structures and $T$-duality

Abstract

This is a short note on generalized $G_2$-structures obtained as a consequence of a $T$-dual construction given in a previous work of the authors together with Leonardo Soriani. Given classical $G_2$-structure on certain seven dimensional manifolds, either closed or co-closed, we obtain integrable generalized $G_2$-structures which are no longer an usual one, and with non-zero three form in general. In particular we obtain manifolds admitting closed generalized $G_2$-structures not admitting closed (usual) $G_2$-structures.

References in corpus (3)

• T-duality for principal torus bundles
• $T$-duality on nilmanifolds
• Construction of Lie algebras with special G2-structures

Cited by in corpus (2)

• $T$-duality on nilmanifolds
• Multiplet Classification of Reducible Verma Modules over the $G_2$ Algebra