Compact self-dual Hermitian surfaces

Apostolov, Vestislav; Davidov, Johann; Muskarov, Oleg

doi:10.1090/S0002-9947-96-01585-1

Compact self-dual Hermitian surfaces
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by Vestislav Apostolov, Johann Davidov and Oleg Muskarov PDF

Trans. Amer. Math. Soc. 348 (1996), 3051-3063 Request permission

Abstract:

In this paper, we obtain a classification (up to conformal equivalence) of the compact self-dual Hermitian surfaces. As an application, we prove that every compact Hermitian surface of pointwise constant holomorphic sectional curvature with respect to either the Riemannian or the Hermitian connection is Kähler.

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