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Hard Lefschetz actions in Riemannian geometry with special holonomy

Conan Leung Chinese Univ of HK Changzheng Li KIAS

Differential Geometry mathscidoc:1608.10088

MRL, 15, 683-698, 2008
It is known that the hard Lefschetz action, together with K¨ahler identities for K¨ahler (resp. hyperk¨ahler) manifolds, determines a su(1, 1)_sup (resp. 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. hyperk¨ahler) manifolds, these symmetries can be enlarged to a so(2, 2)_sup (resp. su(2, 2)_sup) action.
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@inproceedings{conan2008hard,
  title={Hard Lefschetz actions in Riemannian geometry with special holonomy},
  author={Conan Leung, and Changzheng Li},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160831102906265203564},
  booktitle={MRL},
  volume={15},
  pages={683-698},
  year={2008},
}
Conan Leung, and Changzheng Li. Hard Lefschetz actions in Riemannian geometry with special holonomy. 2008. Vol. 15. In MRL. pp.683-698. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160831102906265203564.
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