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A note on fibrations of \(G_2\)-manifolds

  • Zhi Hu
  • Pengfei HuangEmail author
Article
  • 49 Downloads

Abstract

In this note, we first give some constructions of torsion-free \(G_2\)-structures on some topological product manifolds. Then we provide a sufficient condition of 3-Calabi–Yau fibrations for \(G_2\)-manifolds. Next we study the Gukov–Yau–Zaslow horizontal lifting for hyperKähler firbations of \(G_2\)-manifolds, and discuss when the Gukov-Yau-Zaslow metric on this fibration is a \(G_2\)-metric.

Mathematics Subject Classification

53C10 53C25 53C26 53C29 14D06 

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Notes

Acknowledgements

The author Z. Hu would like to thank Dr. Yeping Zhang and Dr. Teng Huang for their discussions. The author P. Huang was financial supported by China Scholarship Council (No. 201706340032). The authors would like to thank the reviewers for their careful reading and useful suggestions.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan
  2. 2.School of MathematicsUniversity of Science and Technology of ChinaHefeiChina
  3. 3.Laboratoire J.A. DieudonnéUniversité Côte d’AzurNiceFrance

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