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PreprintCC BY 4.0arXiv

Strong G2-structures with torsion: a survey and new examples

  • Anna Fino
  • Udhav Fowdar
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Abstract

This article has two main parts. The first consists of a brief survey of G2-structures with torsion, namely G2-structures admitting a G2-connection with totally skew-symmetric torsion. We focus primarily on the strong condition that the associated torsion $3$-form is closed. We review their basic properties and their connections with the heterotic G2 system, generalized geometry, and six-dimensional geometry. In the second part, we construct two complete cohomogeneity-one strong G2T-structures on ℝ× S3× S3 with non-zero closed and co-closed characteristic torsion, and non-vanishing characteristic Ricci tensor. Both have an asymptotically cylindrical end; at the other end, the first is asymptotically conical (AC), with a torsion-free G2 cone as its asymptotic model, while the second is asymptotically locally conical (ALC), with a constant-length circle bundle over a Calabi--Yau cone as its asymptotic model. We investigate the induced SU(3)-structures on their circle quotients and show that they are globally conformally almost Kähler and globally conformally Kähler, respectively. To the best of our knowledge, these provide the first complete strong G2T-structures whose underlying metrics are not locally Riemannian products.

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Cite

BibTeXRIS
BibTeX
@misc{fino2026strong,
  title = {{Strong $G_2$-structures with torsion: a survey and new examples}},
  author = {Anna Fino and Udhav Fowdar},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04460},
  eprint = {2611.04460},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04460},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Strong G_2-structures with torsion: a survey and new examples
AU  - Anna Fino
AU  - Udhav Fowdar
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04460
UR  - https://arxiv.org/abs/2611.04460
AB  - This article has two main parts. The first consists of a brief survey of G_2-structures with torsion, namely G_2-structures admitting a G_2-connection with totally skew-symmetric torsion. We focus primarily on the strong condition that the associated torsion $3$-form is closed. We review their basic properties and their connections with the heterotic G_2 system, generalized geometry, and six-dimensional geometry. In the second part, we construct two complete cohomogeneity-one strong G_2T-structures on ℝ× S^3× S^3 with non-zero closed and co-closed characteristic torsion, and non-vanishing characteristic Ricci tensor. Both have an asymptotically cylindrical end; at the other end, the first is asymptotically conical (AC), with a torsion-free G_2 cone as its asymptotic model, while the second is asymptotically locally conical (ALC), with a constant-length circle bundle over a Calabi--Yau cone as its asymptotic model. We investigate the induced SU(3)-structures on their circle quotients and show that they are globally conformally almost Kähler and globally conformally Kähler, respectively. To the best of our knowledge, these provide the first complete strong G_2T-structures whose underlying metrics are not locally Riemannian products.
ER  -