Open Access
2018 On the curvature of Einstein–Hermitian surfaces
Mustafa Kalafat, Caner Koca
Illinois J. Math. 62(1-4): 25-39 (2018). DOI: 10.1215/ijm/1552442655

Abstract

We give a mathematical exposition of the Page metric, and introduce an efficient coordinate system for it. We carefully examine the submanifolds of the underlying smooth manifold, and show that the Page metric does not have positive holomorphic bisectional curvature. We exhibit a holomorphic subsurface with flat normal bundle. We also give another proof of the fact that a compact complex surface together with an Einstein–Hermitian metric of positive orthogonal bisectional curvature is biholomorphically isometric to the complex projective plane with its Fubini–Study metric up to rescaling. This result relaxes the Kähler condition in Berger’s theorem, and the positivity condition on sectional curvature in a theorem proved by the second author.

Citation

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Mustafa Kalafat. Caner Koca. "On the curvature of Einstein–Hermitian surfaces." Illinois J. Math. 62 (1-4) 25 - 39, 2018. https://doi.org/10.1215/ijm/1552442655

Information

Received: 4 August 2015; Revised: 9 October 2018; Published: 2018
First available in Project Euclid: 13 March 2019

zbMATH: 07036779
MathSciNet: MR3922409
Digital Object Identifier: 10.1215/ijm/1552442655

Subjects:
Primary: 53C25 , 53C55

Rights: Copyright © 2018 University of Illinois at Urbana-Champaign

Vol.62 • No. 1-4 • 2018
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