A note on fibrations of \(G_2\)-manifolds
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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 Classification53C10 53C25 53C26 53C29 14D06
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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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