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Bulletin of the London Mathematical Society 1994 26(2):191-194; doi:10.1112/blms/26.2.191
© 1994 by London Mathematical Society
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© London Mathematical Society

The Hitchin-Thorpe Inequality for Einstein-Weyl Manifolds

Henrik Pedersen, Yat Sun Poon and Andrew Swann

Department of Mathematics, and Computer Science, Odense University 5230 Odense M, Denmark
Department of Mathematics, University of California Riverside, CA 92521, USA

Received 28 September 1992. Revision received 15 February 1993.

An inequality relating the Euler characteristic, the signature and the L2-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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