Scalar-flat Kähler surfaces of all genera.
Jongsu Kim, C., Pontecorvo, M. LeBrun (1997)
Journal für die reine und angewandte Mathematik
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Jongsu Kim, C., Pontecorvo, M. LeBrun (1997)
Journal für die reine und angewandte Mathematik
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Yann Rollin, Michael Singer (2009)
Journal of the European Mathematical Society
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Claude LeBrun (1991)
Journal für die reine und angewandte Mathematik
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Yum-Tong Siu, Paul Yang (1981)
Inventiones mathematicae
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Sai-Kee Yeung (1990)
Inventiones mathematicae
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Claude LeBrun, Michael Singer (1993)
Inventiones mathematicae
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Jeon, Hyang Seon, Pyo, Yong-Soo (2002)
Balkan Journal of Geometry and its Applications (BJGA)
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Guilfoyle, Brendan, Klingenberg, Wilhelm (2008)
Beiträge zur Algebra und Geometrie
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Andrew S. Dancer (1996)
Journal für die reine und angewandte Mathematik
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Włodzimierz Jelonek (2014)
Colloquium Mathematicae
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The aim of this paper is to describe all Kähler manifolds with quasi-constant holomorphic sectional curvature with κ = 0.
Lemence, R.S., Oguro, T., Sekigawa, K. (2004)
International Journal of Mathematics and Mathematical Sciences
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Jaeman Kim (2006)
Czechoslovak Mathematical Journal
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On a 4-dimensional anti-Kähler manifold, its zero scalar curvature implies that its Weyl curvature vanishes and vice versa. In particular any 4-dimensional anti-Kähler manifold with zero scalar curvature is flat.
Simone Calamai, David Petrecca (2017)
Complex Manifolds
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In this short note, we prove that a Calabi extremal Kähler-Ricci soliton on a compact toric Kähler manifold is Einstein. This settles for the class of toric manifolds a general problem stated by the authors that they solved only under some curvature assumptions.