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arXiv · 0808.0393

Hard Lefschetz actions in Riemannian geometry with special holonomy

Naichung Conan Leung·Changzheng Li
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Abstract

It is known that the hard Lefschetz action, together with Kähler identities for Kähler (resp. hyperkähler) manifolds, determines a $\mathfrak{su}(1,1)_{sup}$ (resp. $\mathfrak{sp}(1,1)_{sup}$) Lie superalgebra action on differential forms. In this paper, we explain the geometric origin of this action, and we also generalize it to manifolds with other holonomy groups. For semi-flat Calabi-Yau (resp. hyperkähler) manifolds, these symmetries can be enlarged to a $\mathfrak{so}(2,2)_{sup}$ (resp. $\mathfrak{su}(2,2)_{sup}$) action.

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BibTeXRIS

Naichung Conan Leung, Changzheng Li. 2008-08-04. Hard Lefschetz actions in Riemannian geometry with special holonomy. https://arxiv.org/abs/0808.0393

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