Relevant bibliographies by topics / Kähler- Einstein equation

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters

Academic literature on the topic 'Kähler- Einstein equation'

Author: Grafiati
Published: 6 September 2023

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Journal articles on the topic "Kähler- Einstein equation"

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Zhang, Xi, and Xiangwen Zhang. "Generalized Kähler–Einstein Metrics and Energy Functionals." Canadian Journal of Mathematics 66, no. 6 (2014): 1413–35. http://dx.doi.org/10.4153/cjm-2013-034-3.

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Abstract.In this paper, we consider a generalized Kähler–Einstein equation on a Kähler manifold M. Using the twisted 𝒦–energy introduced by Song and Tian, we show that the existence of generalized Kähler–Einstein metrics with semi–positive twisting (1, 1)–form θ is also closely related to the properness of the twisted 𝒦-energy functional. Under the condition that the twisting form θ is strictly positive at a point or M admits no nontrivial Hamiltonian holomorphic vector field, we prove that the existence of generalized Kähler–Einstein metric implies a Moser–Trudinger type inequality.
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PAN, LISHUANG, AN WANG, and LIYOU ZHANG. "ON THE KÄHLER–EINSTEIN METRIC OF BERGMAN–HARTOGS DOMAINS." Nagoya Mathematical Journal 221, no. 1 (2016): 184–206. http://dx.doi.org/10.1017/nmj.2016.4.

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We study the complete Kähler–Einstein metric of certain Hartogs domains ${\rm\Omega}_{s}$ over bounded homogeneous domains in $\mathbb{C}^{n}$. The generating function of the Kähler–Einstein metric satisfies a complex Monge–Ampère equation with Dirichlet boundary condition. We reduce the Monge–Ampère equation to an ordinary differential equation and solve it explicitly when we take the parameter $s$ for some critical value. This generalizes previous results when the base is either the Euclidean unit ball or a bounded symmetric domain.
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Zhang, Xi. "Hermitian Yang–Mills–Higgs Metrics on Complete Kähler Manifolds." Canadian Journal of Mathematics 57, no. 4 (2005): 871–96. http://dx.doi.org/10.4153/cjm-2005-034-3.

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AbstractIn this paper, first, we will investigate the Dirichlet problem for one type of vortex equation, which generalizes the well-known Hermitian Einstein equation. Secondly, we will give existence results for solutions of these vortex equations over various complete noncompact Kähler manifolds.
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Visinescu, Mihai. "Sasaki–Ricci flow equation on five-dimensional Sasaki–Einstein space Yp,q." Modern Physics Letters A 35, no. 14 (2020): 2050114. http://dx.doi.org/10.1142/s021773232050114x.

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We analyze the transverse Kähler–Ricci flow equation on Sasaki-Einstein space [Formula: see text]. Explicit solutions are produced representing new five-dimensional Sasaki structures. Solutions which do not modify the transverse metric preserve the Sasaki–Einstein feature of the contact structure. If the transverse metric is altered, the deformed metrics remain Sasaki, but not Einstein.
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Alekseevsky, Dmitri V., and Fabio Podestà. "Homogeneous almost-Kähler manifolds and the Chern–Einstein equation." Mathematische Zeitschrift 296, no. 1-2 (2019): 831–46. http://dx.doi.org/10.1007/s00209-019-02446-y.

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ARVANITOYEORGOS, ANDREAS, IOANNIS CHRYSIKOS, and YUSUKE SAKANE. "HOMOGENEOUS EINSTEIN METRICS ON GENERALIZED FLAG MANIFOLDS WITH FIVE ISOTROPY SUMMANDS." International Journal of Mathematics 24, no. 10 (2013): 1350077. http://dx.doi.org/10.1142/s0129167x13500778.

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We construct the homogeneous Einstein equation for generalized flag manifolds G/K of a compact simple Lie group G whose isotropy representation decomposes into five inequivalent irreducible Ad (K)-submodules. To this end, we apply a new technique which is based on a fibration of a flag manifold over another such space and the theory of Riemannian submersions. We classify all generalized flag manifolds with five isotropy summands, and we use Gröbner bases to study the corresponding polynomial systems for the Einstein equation. For the generalized flag manifolds E6/(SU(4) × SU(2) × U(1) × U(1))
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Li, Chi. "On the limit behavior of metrics in the continuity method for the Kähler–Einstein problem on a toric Fano manifold." Compositio Mathematica 148, no. 6 (2012): 1985–2003. http://dx.doi.org/10.1112/s0010437x12000334.

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AbstractThis work is a continuation of the author’s previous paper [Greatest lower bounds on the Ricci curvature of toric Fano manifolds, Adv. Math. 226 (2011), 4921–4932]. On any toric Fano manifold, we discuss the behavior of the limit metric of a sequence of metrics which are solutions to a continuity family of complex Monge–Ampère equations in the Kähler–Einstein problem. We show that the limit metric satisfies a singular complex Monge–Ampère equation. This gives a conic-type singularity for the limit metric. Information on conic-type singularities can be read off from the geometry of the
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SAKAGUCHI, MAKOTO. "FOUR-DIMENSIONAL N=2 SUPERSTRING BACKGROUNDS AND THE REAL HEAVENS." International Journal of Modern Physics A 11, no. 07 (1996): 1279–97. http://dx.doi.org/10.1142/s0217751x96000572.

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We study N=2 superstring backgrounds which are four-dimensional, non-Kählerian and contain nontrivial dilaton and torsion fields. In particular we consider the case where the backgrounds possess at least one U(1) isometry and are characterized by the continual Toda equation and the Laplace equation. We obtain a string background associated with a nontrivial solution of the continual Toda equation, which is mapped, under the T duality transformation, to the Taub-NUT instanton background. It is shown that the integrable property of the non-Kählerian spaces has a direct origin in the real heavens
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Biswas, Indranil. "Yang–Mills connections on compact complex tori." Journal of Topology and Analysis 07, no. 02 (2015): 293–307. http://dx.doi.org/10.1142/s1793525315500107.

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Let G be a connected reductive complex affine algebraic group and K ⊂ G a maximal compact subgroup. Let M be a compact complex torus equipped with a flat Kähler structure and (EG, θ) a polystable Higgs G-bundle on M. Take any C∞ reduction of structure group EK ⊂ EG to the subgroup K that solves the Yang–Mills equation for (EG, θ). We prove that the principal G-bundle EG is polystable and the above reduction EK solves the Einstein–Hermitian equation for EG. We also prove that for a semistable (respectively, polystable) Higgs G-bundle (EG, θ) on a compact connected Calabi–Yau manifold, the under
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ARVANITOYEORGOS, ANDREAS. "GEOMETRY OF FLAG MANIFOLDS." International Journal of Geometric Methods in Modern Physics 03, no. 05n06 (2006): 957–74. http://dx.doi.org/10.1142/s0219887806001399.

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A flag manifold is a homogeneous space M = G/K, where G is a compact semisimple Lie group, and K the centralizer of a torus in G. Equivalently, M can be identified with the adjoint orbit Ad (G)w of an element w in the Lie algebra of G. We present several aspects of flag manifolds, such as their classification in terms of painted Dynkin diagrams, T-roots and G-invariant metrics, and Kähler metrics. We give a Lie-theoretic expression of the Ricci tensor in M, hence reducing the Einstein equation on flag manifolds into an algebraic system of equations, which can be solved in several cases. A flag
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Dissertations / Theses on the topic "Kähler- Einstein equation"

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Yi, Li. "Théorèmes d'extension et métriques de Kähler-Einstein généralisées." Thesis, Université de Lorraine, 2012. http://www.theses.fr/2012LORR0151/document.

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Cette thèse comporte deux parties: - Dans la première partie, nous traitons d'abord une version kahlérienne du célèbre théorème d'extension d'Ohsawa-Takegoshi, puis, un problème de prolongement des courants positifs fermés. Notre motivation provient de la conjecture de Siu sur l'invariance des plurigenres dans le cas d'une famille kahlérienne. En effet, dans la preuve du célèbre théorème d'invariance des plurigenres de Siu, le théorème d'extension d'Ohsawa-Takegoshi joue un rôle important. Il est donc naturel de penser que la preuve de la conjecture fera également intervenir un théorème d'exte
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Book chapters on the topic "Kähler- Einstein equation"

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Siu, Yum-Tong. "The Heat Equation Approach to Hermitian-Einstein Metrics on Stable Bundles." In Lectures on Hermitian-Einstein Metrics for Stable Bundles and Kähler-Einstein Metrics. Birkhäuser Basel, 1987. http://dx.doi.org/10.1007/978-3-0348-7486-1_1.

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Koiso, Norihito. "On Rotationally Symmetric Hamilton's Equation for Kähler-Einstein Metrics." In Recent Topics in Differential and Analytic Geometry. Elsevier, 1990. http://dx.doi.org/10.1016/b978-0-12-001018-9.50015-4.

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LeBrun, Claude. "The Einstein‐Maxwell Equations, Extremal Kähler Metrics, and Seiberg‐Witten Theory." In The Many Facets of Geometry. Oxford University Press, 2010. http://dx.doi.org/10.1093/acprof:oso/9780199534920.003.0003.

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