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Displaying similar documents to “Scalar-flat Kähler metrics on blown-up ruled surfaces.”

Toric Hermitian surfaces and almost Kähler structures

Włodzimierz Jelonek (2007)

Annales Polonici Mathematici

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The aim of this paper is to investigate the class of compact Hermitian surfaces (M,g,J) admitting an action of the 2-torus T² by holomorphic isometries. We prove that if b₁(M) is even and (M,g,J) is locally conformally Kähler and χ(M) ≠ 0 then there exists an open and dense subset U ⊂ M such that ( U , g | U ) is conformally equivalent to a 4-manifold which is almost Kähler in both orientations. We also prove that the class of Calabi Ricci flat Kähler metrics related with the real Monge-Ampère equation...

Toric extremal Kähler-Ricci solitons are Kähler-Einstein

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.