Einstein-Weyl deformations and submanifolds

Henrik Pedersen Yat Sun Poon Andrew Swann

Differential Geometry mathscidoc:1910.43804

International Journal of Mathematics, 7, (5), 705-719, 1996.10
Motivated by new explicit positive Ricci curvature metrics on the four-sphere which are also Einstein-Weyl, we show that the dimension of the Einstein-Weyl moduli near certain Einstein metrics is bounded by the rank of the isometry group and that any Weyl manifold can be embedded as a hypersurface with prescribed second fundamental form in some Einstein-Weyl space. Closed four-dimensional Einstein-Weyl manifolds are proved to be absolute minima of the L<sup>2</sup>-norm of the curvature of Weyl manifolds and a local version of the Lafontaine inequality is obtained. The above metrics on the four-sphere are shown to contain minimal hypersurfaces isometric to S<sup>1</sup>S<sup>2</sup> whose second fundamental form has constant length.
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@inproceedings{henrik1996einstein-weyl,
  title={Einstein-Weyl deformations and submanifolds},
  author={Henrik Pedersen, Yat Sun Poon, and Andrew Swann},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020220725527322333},
  booktitle={International Journal of Mathematics},
  volume={7},
  number={5},
  pages={705-719},
  year={1996},
}
Henrik Pedersen, Yat Sun Poon, and Andrew Swann. Einstein-Weyl deformations and submanifolds. 1996. Vol. 7. In International Journal of Mathematics. pp.705-719. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020220725527322333.
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