Abstract
We prove that the Atiyah-Hitchin-Singer [1] and Eells-Salamon [6] almost-complex structures on the negative twistor space of an oriented Riemannian four-manifold are harmonic in the sense of C. Wood [17, 18] if and only if the base manifold is, respectively, self-dual or self-dual and of constant scalar curvature. The stability of these almost-complex structures is also discussed.
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Research supported in part by the NSF grant INT-9903302. Both authors are members of EDGE, Research Training Network HPRN-CT-2000-00101, supported by the European Human Potential Programme.
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Davidov, J., Muškarov, O. Harmonic almost-complex structures on twistor spaces. Isr. J. Math. 131, 319–332 (2002). https://doi.org/10.1007/BF02785864
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DOI: https://doi.org/10.1007/BF02785864