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<p>We revisit the study of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\textrm{G}_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>G</mtext> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-structures with special torsion, and isolated singularities. Many of the known examples with conical singularities admit additional symmetries, and we describe circle-invariant <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\textrm{G}_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>G</mtext> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-structures in this context. Finally, we show that collapsing the circle fibres of a contact Calabi-Yau manifold at isolated points cannot produce a <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\textrm{G}_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>G</mtext> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-structure with bounded torsion.</p>

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Isolated singularities in \(\textrm{G}_2\)-structures with torsion

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月14日

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  • Henrique Sá Earp,
  • Jakob R. Stein

摘要

We revisit the study of \(\textrm{G}_2\) G 2 -structures with special torsion, and isolated singularities. Many of the known examples with conical singularities admit additional symmetries, and we describe circle-invariant \(\textrm{G}_2\) G 2 -structures in this context. Finally, we show that collapsing the circle fibres of a contact Calabi-Yau manifold at isolated points cannot produce a \(\textrm{G}_2\) G 2 -structure with bounded torsion.