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The algebra of exterior differential forms on a regular 3-Sasakian 7-manifold is investigated, with special reference to nearly-parallel \(G_2\) 3-forms. This is applied to the study of 3-forms invariant under cohomogeneity-one actions by \(SO(4)\) on the 7-sphere and on Berger’s space \(SO(5)/SO(3)\) .

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Revisiting 3-Sasakian and \(G_2\) -structures

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  • 发表日期：

    2025年

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  • Simon Salamon,
  • Ragini Singhal

摘要

The algebra of exterior differential forms on a regular 3-Sasakian 7-manifold is investigated, with special reference to nearly-parallel \(G_2\) 3-forms. This is applied to the study of 3-forms invariant under cohomogeneity-one actions by \(SO(4)\) on the 7-sphere and on Berger’s space \(SO(5)/SO(3)\) .