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The twisted G2 equation for strong G2-structures with torsion Article

Fino, A, Martín-Merchán, L, Raffero, A. (2024). The twisted G2 equation for strong G2-structures with torsion . 20(6), 2711-2767. 10.4310/PAMQ.241112235423

cited authors

  • Fino, A; Martín-Merchán, L; Raffero, A

authors

abstract

  • We discuss general properties of strong G2-structures with torsion and we investigate the twisted G2 equation, which represents the G2-analogue of the twisted Calabi-Yau equation for SU (n)-structures introduced in [18]. In particular, we show that invariant strong G2-structures with torsion do not occur on compact non-flat solvmanifolds. This implies the non-existence of non-trivial solutions to the twisted Calabi-Yau equation on compact solvmanifolds of dimensions 4 and 6. More generally, we prove that a compact, connected homogeneous space admitting invariant strong G2-structures with torsion is diffeomorphic either to S3 ×T4 or to S3 ×S3 ×S1, up to a covering, and that in both cases solutions to the twisted G2 equation exist. Finally, we discuss the behavior of the homogeneous Laplacian coflow forRwaif0fctWvGLMvLNUXRmY7T0apw0uH9strong G2-structures with torsion on these spaces.

publication date

  • January 1, 2024

Digital Object Identifier (DOI)

start page

  • 2711

end page

  • 2767

volume

  • 20

issue

  • 6