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The Hitchin-Thorpe inequality for Einstein-Weyl manifolds

Henrik Pedersen Yat Sun Poon Andrew Swann

Differential Geometry mathscidoc:1910.43809

Bulletin of the London Mathematical Society, 26, (2), 191-194, 1994.3
An inequality relating the Euler characteristic, the signature and the <i>L</i><sub>2</sub>-norm of the curvature of the bundle of densities is proved for a four-dimensional compact Einstein-Weyl manifold. This generalises the Hitchin-Thorpe inequality for Einstein manifolds. The case where equality occurs is discussed and related to Hitchin's classification of Ricci-flat self-dual four-manifolds and to the recent work of Gauduchon on closed non-exact Einstein-Weyl geometries.
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@inproceedings{henrik1994the,
  title={The Hitchin-Thorpe inequality for Einstein-Weyl manifolds},
  author={Henrik Pedersen, Yat Sun Poon, and Andrew Swann},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020220848733108338},
  booktitle={Bulletin of the London Mathematical Society},
  volume={26},
  number={2},
  pages={191-194},
  year={1994},
}
Henrik Pedersen, Yat Sun Poon, and Andrew Swann. The Hitchin-Thorpe inequality for Einstein-Weyl manifolds. 1994. Vol. 26. In Bulletin of the London Mathematical Society. pp.191-194. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020220848733108338.
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