Toric Hermitian surfaces and almost Kähler structures

Włodzimierz Jelonek

Displaying similar documents to “Toric Hermitian surfaces and almost Kähler structures”

Stability under deformations of Hermite-Einstein almost Kähler metrics

Mehdi Lejmi (2014)

Annales de l’institut Fourier

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On a $4$ -dimensional compact symplectic manifold, we consider a smooth family of compatible almost-complex structures such that at time zero the induced metric is Hermite-Einstein almost-Kähler metric with zero or negative Hermitian scalar curvature. We prove, under certain hypothesis, the existence of a smooth family of compatible almost-complex structures, diffeomorphic at each time to the initial one, and inducing constant Hermitian scalar curvature metrics.

A new proof of the existence of Kähler-Einstein metrics on A3, II.

P. Topiwala (1987)

Inventiones mathematicae

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Hermitian curvature flow

Jeffrey Streets, Gang Tian (2011)

Journal of the European Mathematical Society

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We define a functional for Hermitian metrics using the curvature of the Chern connection. The Euler–Lagrange equation for this functional is an elliptic equation for Hermitian metrics. Solutions to this equation are related to Kähler–Einstein metrics, and are automatically Kähler–Einstein under certain conditions. Given this, a natural parabolic flow equation arises. We prove short time existence and regularity results for this flow, as well as stability for the flow near Kähler–Einstein...

Weakly-Einstein hermitian surfaces

Vestislav Apostolov, Oleg Muškarov (1999)

Annales de l'institut Fourier

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A consequence of the Riemannian Goldberg-Sachs theorem is the fact that the Kähler form of an Einstein Hermitian surface is an eigenform of the curvature operator. Referring to this property as we obtain a complete classification of the compact locally homogeneous $*$ -Einstein Hermitian surfaces. We also provide large families of non-homogeneous $*$ -Einstein (but non-Einstein) Hermitian metrics on $ℂ ℙ^{2} ♯ {\overline{ℂ ℙ}}^{2}$ , $ℂ ℙ^{1} \times ℂ ℙ^{1}$ , and on the product surface $X \times Y$ of two curves $X$ and $Y$ whose genuses are greater than 1...

Some critical almost Kähler structures

Takashi Oguro, Kouei Sekigawa (2008)

Colloquium Mathematicae

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We consider the set of all almost Kähler structures (g,J) on a 2n-dimensional compact orientable manifold M and study a critical point of the functional $ℱ_{λ, μ} (J, g) = \int_{M} (λ τ + μ τ *) d M_{g}$ with respect to the scalar curvature τ and the *-scalar curvature τ*. We show that an almost Kähler structure (J,g) is a critical point of $ℱ_{- 1, 1}$ if and only if (J,g) is a Kähler structure on M.

Scalar-flat Kähler metrics on blown-up ruled surfaces.

Claude LeBrun (1991)

Journal für die reine und angewandte Mathematik

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On Kähler-Einstein metrics on certain Kahler manifolds with C1 (M) > 0.

G. Tian (1987)

Inventiones mathematicae

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Holomorphically pseudosymmetric Kähler metrics on ℂℙⁿ

Włodzimierz Jelonek (2012)

Colloquium Mathematicae

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The aim of this paper is to present examples of holomorphically pseudosymmetric Kähler metrics on the complex projective spaces ℂℙⁿ, where n ≥ 2.

Remarks on the Existence Problem of Positive Kähler-Einstein Metrics.

Wei-Yue Ding (1988)

Mathematische Annalen

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Kähler-Einstein metrics: Old and New

Daniele Angella, Cristiano Spotti (2017)

Complex Manifolds

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We present classical and recent results on Kähler-Einstein metrics on compact complex manifolds, focusing on existence, obstructions and relations to algebraic geometric notions of stability (K-stability). These are the notes for the SMI course "Kähler-Einstein metrics" given by C.S. in Cortona (Italy), May 2017. The material is not intended to be original.

Astheno-Kähler structures on Calabi-Eckmann manifolds

Koji Matsuo (2009)

Colloquium Mathematicae

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We show that there exist astheno-Kähler structures on Calabi-Eckmann manifolds.

Deformation of Kähler matrics to Kähler-Eisenstein metrics on compact Kähler manifolds.

Huai-Dong Cao (1985)

Inventiones mathematicae

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3-submersions from QR-hypersurfaces of quaternionic Kähler manifolds

Gabriel Eduard Vîlcu (2010)

Annales Polonici Mathematici

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We study 3-submersions from a QR-hypersurface of a quaternionic Kähler manifold onto an almost quaternionic hermitian manifold. We also prove the non-existence of quaternionic submersions between quaternionic Kähler manifolds which are not locally hyper-Kähler.

Locally conformally Kähler metrics on Hopf surfaces

Paul Gauduchon, Liviu Ornea (1998)

Annales de l'institut Fourier

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A primary Hopf surface is a compact complex surface with universal cover $ℂ^{2} - {(0, 0)}$ and cyclic fundamental group generated by the transformation $(u, v) \mapsto (α u + λ v^{m}, β v)$ , $m \in ℤ$ , and $α, β, λ \in ℂ$ such that $∣ α ∣ \geq ∣ β ∣ > 1$ and $(α - β^{m}) λ = 0$ . Being diffeomorphic with $S^{3} \times S^{1}$ Hopf surfaces cannot admit any Kähler metric. However, it was known that for $λ = 0$ and $∣ α ∣ = ∣ β ∣$ they admit a locally conformally Kähler metric with parallel Lee form. We here provide the construction of a locally conformally Kähler metric with parallel Lee form for primary Hopf surfaces of class $1$ ( $λ = 0$ )....

Canonical metrics on some domains of $ℂ^{n}$

Fabio Zuddas (2008-2009)

Séminaire de théorie spectrale et géométrie

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The study of the existence and uniqueness of a preferred Kähler metric on a given complex manifold $M$ is a very important area of research. In this talk we recall the main results and open questions for the most important canonical metrics (Einstein, constant scalar curvature, extremal, Kähler-Ricci solitons) in the compact and the non-compact case, then we consider a particular class of complex domains $D$ in $ℂ^{n}$ , the so-called Hartogs domains, which can be equipped with a natural Kaehler...