Abstract
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.
Original language | English |
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Journal | Bulletin of the London Mathematical Society |
Volume | 26 |
Issue number | 2 |
Pages (from-to) | 193-194 |
Number of pages | 2 |
ISSN | 0024-6093 |
DOIs | |
Publication status | Published - 1994 |
Externally published | Yes |