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Compact solvmanifolds with calibrated and cocalibrated \mathrm {G}_2-structures

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Compact solvmanifolds with calibrated and cocalibrated \mathrm {G}_2-structures

10$

Víctor Manero 

Abstract

We give a method to obtain new solvable 7-dimensional Lie algebras endowed with closed and coclosed \mathrm {G}_2-structures starting from 6-dimensional solvable Lie algebras with symplectic half-flat and half-flat \mathrm {SU}(3)-structures, respectively. Provided the existence of a lattice for the corresponding Lie groups we obtain new examples of compact solvmanifolds endowed with calibrated and cocalibrated \mathrm {G}_2-structures. As an application of this construction we also obtain a formal compact solvmanifold with first Betti number b_1=1 endowed with a calibrated \mathrm {G}_2-structure and such that does not admit any invariant torsion-free \mathrm {G}_2-structure.

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Year 2020
Language English
Format PDF
DOI 10.1007/s00229-019-01133-w