Transactions of the American Mathematical Society

Author(s): Florin Alexandru Belgun
Journal: Trans. Amer. Math. Soc. 356 (2004), 853-880.
MSC (2000): Primary 53C21, 53A30, 32Qxx
Posted: October 21, 2003
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Abstract: We study complex 4-manifolds with holomorphic self-dual conformal structures, and we obtain an interpretation of the Weyl tensor of such a manifold as the projective curvature of a field of cones on the ambitwistor space. In particular, its vanishing is implied by the existence of some compact, simply-connected, null-geodesics. We also show that the projective structure of the $\beta$ -surfaces of a self-dual manifold is flat. All these results are illustrated in detail in the case of the complexification of $\mathbb{CP} ^2$ .

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 53C21, 53A30, 32Qxx

Florin Alexandru Belgun
Affiliation: Centre de Mathématiques, UMR 7640 CNRS, Ecole Polytechnique, 91128 Palaiseau cedex, France
Address at time of publication: Mathematisches Institut, Augustusplatz 10/11, 04109 Leipzig, Germany
Email: belgun@math.polytechnique.fr, Florin.Belgun@math.uni-leipzig.de

DOI: 10.1090/S0002-9947-03-03157-X
PII: S 0002-9947(03)03157-X
Received by editor(s): February 27, 2000
Posted: October 21, 2003
Copyright of article: Copyright 2003, American Mathematical Society

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