Relevant bibliographies by topics / Kähler metric

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Kähler metric'

Author: Grafiati
Published: 10 March 2023
Last updated: 6 September 2023

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Journal articles on the topic "Kähler metric"

1

Kawamura, Masaya. "On Kähler-like and G-Kähler-like almost Hermitian manifolds." Complex Manifolds 7, no. 1 (April 3, 2020): 145–61. http://dx.doi.org/10.1515/coma-2020-0009.

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AbstractWe introduce Kähler-like, G-Kähler-like metrics on almost Hermitian manifolds. We prove that a compact Kähler-like and G-Kähler-like almost Hermitian manifold equipped with an almost balanced metric is Kähler. We also show that if a Kähler-like and G-Kähler-like almost Hermitian manifold satisfies B_{\bar i\bar j}^\lambda B_{\lambda j}^i \ge 0, then the metric is almost balanced and the almost complex structure is integrable, which means that the metric is balanced. We investigate a G-Kähler-like almost Hermitian manifold under some assumptions.
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Calderbank, David M. J., Vladimir S. Matveev, and Stefan Rosemann. "Curvature and the c-projective mobility of Kähler metrics with hamiltonian 2-forms." Compositio Mathematica 152, no. 8 (April 26, 2016): 1555–75. http://dx.doi.org/10.1112/s0010437x16007302.

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The mobility of a Kähler metric is the dimension of the space of metrics with which it is c-projectively equivalent. The mobility is at least two if and only if the Kähler metric admits a nontrivial hamiltonian 2-form. After summarizing this relationship, we present necessary conditions for a Kähler metric to have mobility at least three: its curvature must have nontrivial nullity at every point. Using the local classification of Kähler metrics with hamiltonian 2-forms, we describe explicitly the Kähler metrics with mobility at least three and hence show that the nullity condition on the curvature is also sufficient, up to some degenerate exceptions. In an appendix, we explain how the classification may be related, generically, to the holonomy of a complex cone metric.
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Hall, Stuart James, and Thomas Murphy. "Numerical Approximations to Extremal Toric Kähler Metrics with Arbitrary Kähler Class." Proceedings of the Edinburgh Mathematical Society 60, no. 4 (January 10, 2017): 893–910. http://dx.doi.org/10.1017/s0013091516000444.

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AbstractWe develop new algorithms for approximating extremal toric Kähler metrics. We focus on an extremal metric on , which is conformal to an Einstein metric (the Chen–LeBrun–Weber metric). We compare our approximation to one given by Bunch and Donaldson and compute various geometric quantities. In particular, we demonstrate a small eigenvalue of the scalar Laplacian of the Einstein metric that gives numerical evidence that the Einstein metric is conformally unstable under Ricci flow.
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Fino, Anna, Gueo Grantcharov, and Luigi Vezzoni. "Astheno–Kähler and Balanced Structures on Fibrations." International Mathematics Research Notices 2019, no. 22 (February 5, 2017): 7093–117. http://dx.doi.org/10.1093/imrn/rnx337.

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Abstract We study the existence of three classes of Hermitian metrics on certain types of compact complex manifolds. More precisely, we consider balanced, strong Kähler with torsion (SKT), and astheno-Kähler metrics. We prove that the twistor spaces of compact hyperkähler and negative quaternionic-Kähler manifolds do not admit astheno-Kähler metrics. Then we provide a construction of astheno-Kähler structures on torus bundles over Kähler manifolds leading to new examples. In particular, we find examples of compact complex non-Kähler manifolds which admit a balanced and an astheno-Kähler metric, thus answering to a question in [52] (see also [24]). One of these examples is simply connected. We also show that the Lie groups SU(3) and G2 admit SKT and astheno-Kähler metrics, which are different. Furthermore, we investigate the existence of balanced metrics on compact complex homogeneous spaces with an invariant volume form, showing in particular that if a compact complex homogeneous space M with invariant volume admits a balanced metric, then its first Chern class c1(M) does not vanish. Finally we characterize Wang C-spaces admitting SKT metrics.
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DUNAJSKI, MACIEJ, and PAUL TOD. "Four–dimensional metrics conformal to Kähler." Mathematical Proceedings of the Cambridge Philosophical Society 148, no. 3 (January 5, 2010): 485–503. http://dx.doi.org/10.1017/s030500410999048x.

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AbstractWe derive some necessary conditions on a Riemannian metric (M, g) in four dimensions for it to be locally conformal to Kähler. If the conformal curvature is non anti–self–dual, the self–dual Weyl spinor must be of algebraic type D and satisfy a simple first order conformally invariant condition which is necessary and sufficient for the existence of a Kähler metric in the conformal class. In the anti–self–dual case we establish a one to one correspondence between Kähler metrics in the conformal class and non–zero parallel sections of a certain connection on a natural rank ten vector bundle over M. We use this characterisation to provide examples of ASD metrics which are not conformal to Kähler.We establish a link between the ‘conformal to Kähler condition’ in dimension four and the metrisability of projective structures in dimension two. A projective structure on a surface U is metrisable if and only if the induced (2, 2) conformal structure on M = TU admits a Kähler metric or a para–Kähler metric.
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Fujiki, Akira. "Remarks on extremal Kähler metrics on ruled manifolds." Nagoya Mathematical Journal 126 (June 1992): 89–101. http://dx.doi.org/10.1017/s0027763000004001.

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Let X be a compact Kähler manifold and γ Kähler class. For a Kàhler metric g on X we denote by Rg the scalar curvature on X According to Calabi [3][4], consider the functional defined on the set of all the Kähler metrics g whose Kähler forms belong to γ, where dvg is the volume form associated to g. Such a Kähler metric is called extremal if it gives a critical point of Ф. In particular, if Rg is constant, g is extremal. The converse is also true if dim L(X) = 0, where L(X) is the maximal connected linear algebraic subgroup of AutoX (cf. [5]). Note also that any Kähler-Einstein metric is of constant scalar curvature.
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SIMANCA, SANTIAGO R. "PRECOMPACTNESS OF THE CALABI ENERGY." International Journal of Mathematics 07, no. 02 (April 1996): 245–54. http://dx.doi.org/10.1142/s0129167x96000141.

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For any complex manifold of Kähler type, the L2-norm of the scalar curvature of an extremal Kähler metric is a continuous function of the Kähler class. In particular, if a convergent sequence of Kähler classes are represented by extremal Kähler metrics, the corresponding sequence of L2-norms of the scalar curvatures is convergent. Similarly, the sequence of holomorphic vector fields associated with a sequence of extremal Kähler metrics with converging Kähler classes is convergent.
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Borówka, Aleksandra. "Quaternion-Kähler manifolds near maximal fixed point sets of $$S^1$$-symmetries." Annali di Matematica Pura ed Applicata (1923 -) 199, no. 3 (October 17, 2019): 1243–62. http://dx.doi.org/10.1007/s10231-019-00920-2.

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Abstract Using quaternionic Feix–Kaledin construction, we provide a local classification of quaternion-Kähler metrics with a rotating $$S^1$$S1-symmetry with the fixed point set submanifold S of maximal possible dimension. For any real-analytic Kähler manifold S equipped with a line bundle with a real-analytic unitary connection with curvature proportional to the Kähler form, we explicitly construct a holomorphic contact distribution on the twistor space obtained by the quaternionic Feix–Kaledin construction from these data. Conversely, we show that quaternion-Kähler metrics with a rotating $$S^1$$S1-symmetry induce on the fixed point set of maximal dimension a Kähler metric together with a unitary connection on a holomorphic line bundle with curvature proportional to the Kähler form and the two constructions are inverse to each other. Moreover, we study the case when S is compact, showing that in this case the quaternion-Kähler geometry is determined by the Kähler metric on the fixed point set (of maximal possible dimension) and by the contact line bundle along the corresponding submanifold on the twistor space. Finally, we relate the results to the c-map construction showing that the family of quaternion-Kähler manifolds obtained from a fixed Kähler metric on S by varying the line bundle and the hyperkähler manifold obtained by hyperkähler Feix–Kaledin construction from S are related by hyperkähler/quaternion-Kähler correspondence.
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Guenancia, Henri. "Kähler–Einstein metrics: From cones to cusps." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 759 (February 1, 2020): 1–27. http://dx.doi.org/10.1515/crelle-2018-0001.

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AbstractIn this note, we prove that on a compact Kähler manifold \hskip-0.569055pt{X}\hskip-0.569055pt carrying a smooth divisor D such that {K_{X}+D} is ample, the Kähler–Einstein cusp metric is the limit (in a strong sense) of the Kähler–Einstein conic metrics when the cone angle goes to 0. We further investigate the boundary behavior of those and prove that the rescaled metrics converge to a cylindrical metric on {\mathbb{C}^{*}\times\mathbb{C}^{n-1}}.
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RUAN, WEI-DONG. "DEGENERATION OF KÄHLER–EINSTEIN MANIFOLDS I: THE NORMAL CROSSING CASE." Communications in Contemporary Mathematics 06, no. 02 (April 2004): 301–13. http://dx.doi.org/10.1142/s0219199704001331.

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In this paper we prove that the Kähler–Einstein metrics for a degeneration family of Kähler manifolds with ample canonical bundles converge in the sense of Cheeger–Gromov to the complete Kähler–Einstein metric on the smooth part of the central fiber when the central fiber has only normal crossing singularities inside smooth total space. We also prove the incompleteness of the Weil–Peterson metric in this case.
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Dissertations / Theses on the topic "Kähler metric"

1

MOSSA, ROBERTO. "Balanced metrics on complex vector bundles and the diastatic exponential of a symmetric space." Doctoral thesis, Università degli Studi di Cagliari, 2011. http://hdl.handle.net/11584/266274.

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This thesis deals with two different subjects: balanced metrics on complex vector bundles and the diastatic exponential of a symmetric space. Correspondingly we have two main results. In the first one we prove that if a holomorphic vector bundle E over a compact Kähler manifold (M,ω) admits a ω-balanced metric then this metric is unique. In the second one, after defining the diastatic exponential of a real analytic Kähler manifold, we prove that for every point p of an Hermitian symmetric space of noncompact type there exists a globally defined diastatic exponential centered in p which is a diffeomorphism and it is uniquely determined by its restriction to polydisks.
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Frost, George. "The projective parabolic geometry of Riemannian, Kähler and quaternion-Kähler metrics." Thesis, University of Bath, 2016. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.690742.

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We present a uniform framework generalising and extending the classical theories of projective differential geometry, c-projective geometry, and almost quaternionic geometry. Such geometries, which we call \emph{projective parabolic geometries}, are abelian parabolic geometries whose flat model is an R-space $G\cdot\mathfrak{p}$ in the infinitesimal isotropy representation $\mathbb{W}$ of a larger self-dual symmetric R-space $H\cdot\mathfrak{q}$. We also give a classification of projective parabolic geometries with $H\cdot\mathfrak{q}$ irreducible which, in addition to the aforementioned classical geometries, includes a geometry modelled on the Cayley plane $\mathbb{OP}^2$ and conformal geometries of various signatures. The larger R-space $H\cdot\mathfrak{q}$ severely restricts the Lie-algebraic structure of a projective parabolic geometry. In particular, by exploiting a Jordan algebra structure on $\mathbb{W}$, we obtain a $\mathbb{Z}^2$-grading on the Lie algebra of $H$ in which we have tight control over Lie brackets between various summands. This allows us to generalise known results from the classical theories. For example, which riemannian metrics are compatible with the underlying geometry is controlled by the first BGG operator associated to $\mathbb{W}$. In the final chapter, we describe projective parabolic geometries admitting a $2$-dimensional family of compatible metrics. This is the usual setting for the classical projective structures; we find that many results which hold in these settings carry over with little to no changes in the general case.
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SALIS, FILIPPO. "The geometry of rotation invariant Kähler metrics." Doctoral thesis, Università degli Studi di Cagliari, 2018. http://hdl.handle.net/11584/255956.

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The present thesis consists of three results related to the geometry of rotation invariant Kähler metrics. In the first one, we prove that a 3-codimensional Kähler-Einstein submanifold of the complex projective space with rotation invariant metric is forced to be the product of complex projective spaces. In the second one, we prove that the only stable-projectively induced Ricci-flat Kähler metrics are flat. Finally, we prove as third result that given a Ricciflat radial Kähler metric defined on a complex surface such that the third coefficient of its Tian-Yau-Zelditch expansion vanishes, then it is flat.
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CANNAS, AGHEDU FRANCESCO. "Quantizations of Kähler metrics on blow-ups." Doctoral thesis, Università degli Studi di Cagliari, 2021. http://hdl.handle.net/11584/309588.

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The thesis consists of three main results related to Kähler metrics on blow-ups. In the first one, we prove that the blow-up C ̃^2 of C^2 at the origin endowed with the Burns–Simanca metric g_BS admits a regular quantization. We use this fact to prove that all coefficients in the Tian-Yau-Catlin-Zelditch expansion for the Burns–Simanca metric vanish and that a dense subset of (C ̃^2,g_BS) admits a Berezin quantization. In the second one, we prove that the generalized Simanca metric on the blow-up C ̃^n of C^n at the origin is projectively induced but not balanced for any integer n>=3. Finally, we prove as third result that any positive integer multiple of the Eguchi–Hanson metric, defined on a dense subset of C ̃^2/Z_2, is not balanced.
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Istrati, Nicolina. "Conformal structures on compact complex manifolds." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCC054/document.

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Dans cette thèse on s’intéresse à deux types de structures conformes non-dégénérées sur une variété complexe compacte donnée. La première c’est une forme holomorphe symplectique twistée (THS), i.e. une deux-forme holomorphe non-dégénérée à valeurs dans un fibré en droites. Dans le deuxième contexte, il s’agit des métriques localement conformément kähleriennes (LCK). Dans la première partie, on se place sur un variété de type Kähler. Les formes THS généralisent les formes holomorphes symplectiques, dont l’existence équivaut à ce que la variété admet une structure hyperkählerienne, par un théorème de Beauville. On montre un résultat similaire dans le cas twisté, plus précisément: une variété compacte de type kählerien qui admet une structure THS est un quotient fini cyclique d’une variété hyperkählerienne. De plus, on étudie sous quelles conditions une variété localement hyperkählerienne admet une structure THS. Dans la deuxième partie, les variétés sont supposées de type non-kählerien. Nous présentons quelques critères pour l’existence ou non-existence de métriques LCK spéciales, en terme du groupe de biholomorphismes de la variété. En outre, on étudie le problème d’irréductibilité analytique des variétés LCK, ainsi que l’irréductibilité de la connexion de Weyl associée. Dans un troisième temps, nous étudions les variétés LCK toriques, qui peuvent être définies en analogie avec les variétés de Kähler toriques. Nous montrons qu’une variété LCK torique compacte admet une métrique de Vaisman torique, ce qui mène à une classification de ces variétés par le travail de Lerman. Dans la dernière partie, on s’intéresse aux propriétés cohomologiques des variétés d’Oeljeklaus-Toma (OT). Plus précisément, nous calculons leur cohomologie de de Rham et celle twistée. De plus, on démontre qu’il existe au plus une classe de de Rham qui représente la forme de Lee d’une métrique LCK sur un variété OT. Finalement, on détermine toutes les classes de cohomologie twistée des métriques LCK sur ces variétés
In this thesis, we are concerned with two types of non-degenerate conformal structures on a given compact complex manifold. The first structure we are interested in is a twisted holomorphic symplectic (THS) form, i.e. a holomorphic non-degenerate two-form valued in a line bundle. In the second context, we study locally conformally Kähler (LCK) metrics. In the first part, we deal with manifolds of Kähler type. THS forms generalise the well-known holomorphic symplectic forms, the existence of which is equivalent to the manifold admitting a hyperkähler structure, by a theorem of Beauville. We show a similar result in the twisted case, namely: a compact manifold of Kähler type admitting a THS structure is a finite cyclic quotient of a hyperkähler manifold. Moreover, we study under which conditions a locally hyperkähler manifold admits a THS structure. In the second part, manifolds are supposed to be of non-Kähler type. We present a few criteria for the existence or non-existence for special LCK metrics, in terms of the group of biholomorphisms of the manifold. Moreover, we investigate the analytic irreducibility issue for LCK manifolds, as well as the irreducibility of the associated Weyl connection. Thirdly, we study toric LCK manifolds, which can be defined in analogy with toric Kähler manifolds. We show that a compact toric LCK manifold always admits a toric Vaisman metric, which leads to a classification of such manifolds by the work of Lerman. In the last part, we study the cohomological properties of Oeljeklaus-Toma (OT) manifolds. Namely, we compute their de Rham and twisted cohomology. Moreover, we prove that there exists at most one de Rham class which represents the Lee form of an LCK metric on an OT manifold. Finally, we determine all the twisted cohomology classes of LCK metrics on these manifolds
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Sektnan, Lars Martin. "Poincaré type Kähler metrics and stability on toric varieties." Thesis, Imperial College London, 2016. http://hdl.handle.net/10044/1/43380.

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In this thesis we study the relationship between the existence of extremal Kähler metrics and stability. We introduce a space of symplectic potentials for toric manifolds, which we show gives metrics with mixed Poincaré type and cone angle singularities. We show uniqueness and that existence implies stability for extremal metrics arising from these potentials. For quadrilaterals, we give a computable criterion for stability in certain cases, giving a definite log-stable region for generic quadrilaterals. We use computational tools to find new examples of stable and unstable toric manifolds. For Poincaré type manifolds with an S1-action, we prove a version of the LeBrun-Simanca openness theorem and Arezzo-Pacard blow-up theorem.
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Rubinstein, Yanir Akiva. "Geometric quantization and dynamical constructions on the space of Kähler metrics." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/44270.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.
Includes bibliographical references (p. 185-200).
This Thesis is concerned with the study of the geometry and structure of the space of Kihler metrics representing a fixed cohomology class on a compact Kähler manifold. The first part of the Thesis is concerned with a problem of geometric quantization: Can the geometry of the infinite-dimensional space of Kähler metrics be approximated in terms of the geometry of the finite-dimensional spaces of FubiniStudy Bergman metrics sitting inside it? We restrict to toric varieties and prove the following result: Given a compact Riemannian manifold with boundary and a smooth map from its boundary into the space of toric Kähler metrics there exists a harmonic map from the manifold with these boundary values and, up to the first two derivatives, it is the limit of harmonic maps from the Riemannian manifold into the spaces of Bergman metrics. This generalizes previous work of Song-Zelditch on geodesics in the space of toric Kähler metrics. In the second part of the Thesis we propose the study of certain discretizations of geometric evolution equations as an approach to the study of the existence problem of some elliptic partial differential equations of a geometric nature as well as a means to obtain interesting dynamical systems on certain infinite-dimensional spaces. We illustrate the fruitfulness of this approach in the context of the Ricci flow as well as another flow on the space of Kähler metrics. We introduce and study dynamical systems related to the Ricci operator on the space of Kähler metrics that arise as discretizations of these flows. As an application, we address several questions in Kähler geometry related to canonical metrics, energy functionals, the Moser-Trudinger-Onofri inequality, Nadel-type multiplier ideal sheaves, and the structure of the space of Kähler metrics.
by Yanir Akiva Rubinstein.
Ph.D.
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Wu, Damin Ph D. Massachusetts Institute of Technology. "Higher canonical asymptotics of Kähler-Einstein metrics on quasi-projective manifolds." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/33600.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.
Includes bibliographical references (p. 61-64).
In this thesis, we derive the asymptotic expansion of the Kiihler-Einstein metrics on certain quasi-projective varieties, which can be compactified by adding a divisor with simple normal crossings. The weighted Cheng-Yau Hilder spaces and the log-filtrations based on the bounded geometry are introduced to characterize the asymptotics. We first develop the analysis of the Monge-Ampere operators on these weighted spaces. We construct a family of linear elliptic operators which can be viewed as certain conjugacies of the specially linearized Monge-Ampbre operators. We derive a theorem of Fredholm alternative for such elliptic operators by the Schauder theory and Yau's generalized maximum principle. Together these results derive the isomorphism theorems of the Monge-Ampbre operators, which imply that the Monge-Ampere operators preserve the log-filtration of the Cheng-Yau Holder ring. Next, by choosing a canonical metric on the submanifold, we construct an initial Kidhler metric on the quasi-projective manifold such that the unique solution of the Monge-Ampere equation belongs to the weighted -1 Cheng-Yau Hölder ring. Moreover, we generalize the Fefferman's operator to act on the volume forms and obtain an iteration formula.
(cont.) Finally, with the aid of the isomorphism theorems and the iteration formula we derive the desired asymptotics from the initial metric. Furthermore, we prove that the obtained asymptotics is canonical in the sense that it is independent of the extensions of the canonical metric on the submanifold.
by Damin Wu.
Ph.D.
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Ben, Ahmed Ali. "Géométrie et dynamique des structures Hermite-Lorentz." Thesis, Lyon, École normale supérieure, 2013. http://www.theses.fr/2013ENSL0824.

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Dans la veine du programme d'Erlangen de Klein, travaux d'E. Cartan, M. Gromov, et d'autres, ce travail se trouve à cheval, entre la géométrie et les actions de groupes. Le thème global serait de comprendre les groupes d'isométries des variétés pseudo-riemanniennes. Plus précisément, suivant une "conjecture vague" de Gromov, classifier les variétés pseudo-riemanniennes dont le groupe d'isométries agit non-proprement, i.e. que son action ne préserve pas de métrique riemannienne auxiliaire?Plusieurs travaux ont été accomplis dans le cas des métriques lorentziennes (i.e. de signature (- +...+)). En revanche, le cas pseudo-riemannien général semble hors de portée.Les structures Hermite-Lorentz se trouvent entre le cas lorentzien et le premier cas pseudo-riemannien général, i.e. de signature (- - +…+). De plus, elle se définit sur des variétés complexes, et promet une extra-rigidité. Plus précisément, une structure Hermite-Lorentz sur une variété complexe consiste en une métrique pseudo-riemannienne de signature (- - +…+) qui est hermitienne au sens qu'elle est invariante par la structure presque complexe. Par analogie au cas hermitien classique, on définit naturellement une notion de métrique Kähler-Lorentz.Comme exemple, on a l'espace de Minkowski complexe ; dans un certain sens, on a un temps de dimension 1 complexe (du point de vue réel, le temps est 2-dimensionnel). On a également l'espace de Sitter et anti de Sitter complexes. Ils ont une courbure holomorphe constante, et généralisent dans ce sens les espaces projectifs et hyperboliques complexes.Cette thèse porte sur les variétés Hermite-Lorentz homogènes. En plus des exemples cités, il y a deux autres espaces symétriques, qui peuvent naturellement jouer le rôle de complexification des espaces de Sitter et anti de Sitter réels.Le résultat principal de la thèse est un théorème de rigidité de ces espaces symétriques : tout espace Hermite-Lorentz homogène à isotropie irréductible est l'un des cinq espaces symétriques précédents. D'autres résultats concernent le cas où l'on remplace l'hypothèse d'irréductibilité par le fait que le groupe d'isométries soit semi-simple
In the vein of Klein's Erlangen program, the research works of E. Cartan, M.Gromov and others, this work straddles between geometry and group actions. The overall theme is to understand the isometry groups of pseudo-Riemannian manifolds. Precisely, following a "vague conjecture" of Gromov, our aim is to classify Pseudo-Riemannian manifolds whose isometry group act’s not properly, i.e that it’s action does not preserve any auxiliary Riemannian metric. Several studies have been made in the case of the Lorentzian metrics (i.e of signature (- + .. +)). However, general pseudo-Riemannian case seems out of reach. The Hermite-Lorentz structures are between the Lorentzian case and the former general pseudo-Riemannian, i.e of signature (- -+ ... +). In addition, it’s defined on complex manifolds, and promises an extra-rigidity. More specifically, a Hermite-Lorentz structure on a complex manifold is a pseudo-Riemannian metric of signature (- -+ ... +), which is Hermitian in the sense that it’s invariant under the almost complex structure. By analogy with the classical Hermitian case, we naturally define a notion of Kähler-Lorentz metric. We cite as example the complex Minkowski space in where, in a sense, we have a one-dimensional complex time (the real point of view, the time is two-dimensional). We cite also the de Sitter and Anti de Sitter complex spaces. They have a constant holomorphic curvature, and generalize in this direction the projective and complex hyperbolic spaces.This thesis focuses on the Hermite-Lorentz homogeneous spaces. In addition with given examples, two other symmetric spaces can naturally play the role of complexification of the de Sitter and anti de Sitter real spaces.The main result of the thesis is a rigidity theorem of these symmetric spaces: any space Hermite-Lorentz isotropy irreducible homogeneous is one of the five previous symmetric spaces. Other results concern the case where we replace the irreducible hypothesis by the fact that the isometry group is semisimple
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Delgove, François. "Sur la géométrie des solitons de Kähler-Ricci dans les variétés toriques et horosphériques." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLS084/document.

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Cette thèse traite des solitons de Kähler-Ricci qui sont des généralisations naturelles des métriques de Kähler-Einstein. Elle est divisée en deux parties. La première étudie la décomposition solitonique de l’espace des champs de vecteurs holomorphes dans le cas des variétés toriques. La seconde partie étudie de manière analytique les variétés horosphériques en redémontrant par la méthode de la continuité l’existence de solitons de Kähler-Ricci sur ces variétés et en calculant après la borne supérieure de Ricci
This thesis deal with Kähler-Ricci solitons which are natural generalizations of Kähler-Einstein metrics. It is divided into two parts. The first one studies the solitonic decomposition of the space of holomorphic vector spaces in the case of toric manifold. The second one studies is an analytic way the existence of horospherical Kähler-Ricci solitons on those manifolds and then computes the greatest Ricci lower bound
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Books on the topic "Kähler metric"

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Takushiro, Ochiai, ed. Kähler metric and moduli spaces. Boston: Academic Press, 1990.

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Tian, Gang. Canonical Metrics in Kähler Geometry. Basel: Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-8389-4.

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Futaki, Akito. Kähler-Einstein Metrics and Integral Invariants. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0078084.

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Faulk, Mitchell. Some canonical metrics on Kähler orbifolds. [New York, N.Y.?]: [publisher not identified], 2019.

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Mabuchi, Toshiki. Test Configurations, Stabilities and Canonical Kähler Metrics. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0500-0.

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Cheltsov, Ivan, Xiuxiong Chen, Ludmil Katzarkov, and Jihun Park, eds. Birational Geometry, Kähler–Einstein Metrics and Degenerations. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-17859-7.

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Siu, Yum-Tong. Lectures on Hermitian-Einstein Metrics for Stable Bundles and Kähler-Einstein Metrics. Basel: Birkhäuser Basel, 1987. http://dx.doi.org/10.1007/978-3-0348-7486-1.

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Kamada, Hiroyuki. Self-dual Kähler metrics of neutral signature on complex surfaces. Sendai, Japan: Tohoku University, 2002.

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9

Complex Monge-Ampère equations and geodesics in the space of Kähler metrics. Berlin: Springer Verlag, 2012.

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Guedj, Vincent, ed. Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-23669-3.

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Book chapters on the topic "Kähler metric"

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Chen, Xiuxiong, and Song Sun. "Space of Kähler Metrics (V) – Kähler Quantization." In Metric and Differential Geometry, 19–41. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0257-4_2.

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Nakajima, Hiraku. "Hyper-Kähler metric on (ℂ²)^{[𝕟]}." In University Lecture Series, 29–46. Providence, Rhode Island: American Mathematical Society, 1999. http://dx.doi.org/10.1090/ulect/018/04.

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Gerchkovitz, Efrat, and Zohar Komargodski. "Sphere Partition Functions and the Kähler Metric on the Conformal Manifold." In Springer Proceedings in Mathematics & Statistics, 101–10. Singapore: Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-2636-2_7.

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Shigekawa, Ichiro, and Setsuo Taniguchi. "A Kähler metric on a based loop group and a covariant differentiation." In Itô’s Stochastic Calculus and Probability Theory, 327–46. Tokyo: Springer Japan, 1996. http://dx.doi.org/10.1007/978-4-431-68532-6_21.

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Schumacher, Georg. "The Curvature of the Petersson-Weil Metric on the Moduli Space of Kähler-Einstein Manifolds." In Complex Analysis and Geometry, 339–54. Boston, MA: Springer US, 1993. http://dx.doi.org/10.1007/978-1-4757-9771-8_14.

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Futaki, Akito. "Kähler-Einstein metrics and extremal Kähler metrics." In Lecture Notes in Mathematics, 31–45. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0078087.

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Tian, Gang. "Extremal Kähler metrics." In Canonical Metrics in Kähler Geometry, 11–21. Basel: Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-8389-4_2.

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Aubin, Thierry. "Einstein-Kähler Metrics." In Some Nonlinear Problems in Riemannian Geometry, 251–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-13006-3_7.

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Mabuchi, Toshiki. "Canonical Kähler Metrics." In SpringerBriefs in Mathematics, 21–24. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0500-0_3.

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Calabi, Eugenio. "Extremal Kähler Metrics II." In Differential Geometry and Complex Analysis, 95–114. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-69828-6_8.

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Conference papers on the topic "Kähler metric"

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NITTA, TAKASHI, and TADASHI TANIGUCHI. "Sp(1)n-INVARIANT QUATERNIONIC KÄHLER METRIC." In Proceedings of the Second Meeting. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812810038_0017.

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TEOFILOVA, M. "LIE GROUPS AS FOUR-DIMENSIONAL CONFORMAL KÄHLER MANIFOLDS WITH NORDEN METRIC." In Proceedings of the 8th International Workshop on Complex Structures and Vector Fields. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812709806_0034.

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MANEV, M., K. GRIBACHEV, and D. MEKEROV. "ON THREE-PARAMETRIC LIE GROUPS AS QUASI-KÄHLER MANIFOLDS WITH KILLING NORDEN METRIC." In Proceedings of the 8th International Workshop on Complex Structures and Vector Fields. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812709806_0022.

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MANEV, M., and M. TEOFILOVA. "ON THE CURVATURE PROPERTIES OF REAL TIME-LIKE HYPERSURFACES OF KÄHLER MANIFOLDS WITH NORDEN METRIC." In Proceedings of 9th International Workshop on Complex Structures, Integrability and Vector Fields. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814277723_0020.

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GRAMCHEV, Todor, and Andrea LOI. "TYZ EXPANSIONS FOR SOME ROTATION INVARIANT KÄHLER METRICS." In Proceedings of the 2nd International Colloquium on Differential Geometry and Its Related Fields. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814355476_0006.

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Tian, G., and S. T. Yau. "Existence of Kähler-Einstein metrics on complete Kähler manifolds and their applications to algebraic geometry." In Proceedings of the Conference on Mathematical Aspects of String Theory. WORLD SCIENTIFIC, 1987. http://dx.doi.org/10.1142/9789812798411_0028.

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Fu, Jixiang. "On non-Kähler Calabi-Yau Threefolds with Balanced Metrics." In Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). Published by Hindustan Book Agency (HBA), India. WSPC Distribute for All Markets Except in India, 2011. http://dx.doi.org/10.1142/9789814324359_0070.

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Pacard, Frank. "Constant Scalar Curvature and Extremal Kähler Metrics on Blow ups." In Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). Published by Hindustan Book Agency (HBA), India. WSPC Distribute for All Markets Except in India, 2011. http://dx.doi.org/10.1142/9789814324359_0078.

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FERNÁNDEZ, M., V. MUÑOZ, and J. A. SANTISTEBAN. "SYMPLECTICALLY ASPHERICAL MANIFOLDS WITH NONTRIVIAL π2 AND WITH NO KÄHLER METRICS." In Proceedings of the Workshop. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812703088_0010.

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KAMADA, HIROYUKI. "EXISTENCE OF INDEFINITE KÄHLER METRICS OF CONSTANT SCALAR CURVATURE ON COMPACT COMPLEX SURFACES." In Proceedings of the 7th International Workshop on Complex Structures and Vector Fields. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701763_0011.

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Reports on the topic "Kähler metric"

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Abreu, Miguel. Toric Kähler Metrics: Cohomogeneity One Examples of Constant Scalar Curvature in Action- Angle Coordinates. GIQ, 2012. http://dx.doi.org/10.7546/giq-11-2010-11-41.

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Abreu, Miguel. Toric Kähler Metrics: Cohomogeneity One Examples of Constant Scalar Curvature in Action-Angle Coordinates. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-17-2010-1-33.

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