Relevant bibliographies by topics / Non-Kähler geometry

Academic literature on the topic 'Non-Kähler geometry'

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Published: 7 September 2024

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Journal articles on the topic "Non-Kähler geometry"

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Dai, Song. "Lower order tensors in non-Kähler geometry and non-Kähler geometric flow." Annals of Global Analysis and Geometry 50, no. 4 (June 6, 2016): 395–418. http://dx.doi.org/10.1007/s10455-016-9518-0.

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Broder, Kyle. "The Schwarz lemma in Kähler and non-Kähler geometry." Asian Journal of Mathematics 27, no. 1 (2023): 121–34. http://dx.doi.org/10.4310/ajm.2023.v27.n1.a5.

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Fino, Anna, and Adriano Tomassini. "Non-Kähler solvmanifolds with generalized Kähler structure." Journal of Symplectic Geometry 7, no. 2 (2009): 1–14. http://dx.doi.org/10.4310/jsg.2009.v7.n2.a1.

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Verbitsky, M. S., V. Vuletescu, and L. Ornea. "Classification of non-Kähler surfaces and locally conformally Kähler geometry." Russian Mathematical Surveys 76, no. 2 (April 1, 2021): 261–89. http://dx.doi.org/10.1070/rm9858.

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Zheng, Fangyang. "Some recent progress in non-Kähler geometry." Science China Mathematics 62, no. 11 (May 22, 2019): 2423–34. http://dx.doi.org/10.1007/s11425-019-9528-1.

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Alessandrini, Lucia, and Giovanni Bassanelli. "Positive $$\partial \bar \partial - closed$$ currents and non-Kähler geometrycurrents and non-Kähler geometry." Journal of Geometric Analysis 2, no. 4 (July 1992): 291–316. http://dx.doi.org/10.1007/bf02934583.

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Cortés, Vicente, and Liana David. "Twist, elementary deformation and K/K correspondence in generalized geometry." International Journal of Mathematics 31, no. 10 (September 2020): 2050078. http://dx.doi.org/10.1142/s0129167x20500780.

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We define the conformal change and elementary deformation in generalized complex geometry. We apply Swann’s twist construction to generalized (almost) complex and Hermitian structures obtained by these operations and establish conditions for the Courant integrability of the resulting twisted structures. We associate to any appropriate generalized Kähler manifold [Formula: see text] with a Hamiltonian Killing vector field a new generalized Kähler manifold, depending on the choice of a pair of non-vanishing functions and compatible twist data. We study this construction when [Formula: see text] is toric, with emphasis on the four-dimensional case, and we apply it to deformations of the standard flat Kähler metric on [Formula: see text], the Fubini–Study metric on [Formula: see text] and the admissible Kähler metrics on Hirzebruch surfaces. As a further application, we recover the K/K (Kähler/Kähler) correspondence, by specializing to ordinary Kähler manifolds.
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Dunajski, Maciej. "Null Kähler Geometry and Isomonodromic Deformations." Communications in Mathematical Physics 391, no. 1 (December 8, 2021): 77–105. http://dx.doi.org/10.1007/s00220-021-04270-0.

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AbstractWe construct the normal forms of null-Kähler metrics: pseudo-Riemannian metrics admitting a compatible parallel nilpotent endomorphism of the tangent bundle. Such metrics are examples of non-Riemannian holonomy reduction, and (in the complexified setting) appear on the space of Bridgeland stability conditions on a Calabi–Yau threefold. Using twistor methods we show that, in dimension four—where there is a connection with dispersionless integrability—the cohomogeneity-one anti-self-dual null-Kähler metrics are generically characterised by solutions to Painlevé I or Painlevé II ODEs.
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YANG, BO. "A CHARACTERIZATION OF NONCOMPACT KOISO-TYPE SOLITONS." International Journal of Mathematics 23, no. 05 (May 2012): 1250054. http://dx.doi.org/10.1142/s0129167x12500541.

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We construct complete gradient Kähler–Ricci solitons of various types on the total spaces of certain holomorphic line bundles over compact Kähler–Einstein manifolds with positive scalar curvature. Those are noncompact analogues of the compact examples found by Koiso [On rotationally symmetric Hamilton's equations for Kähler–Einstein metrics, in Recent Topics in Differential and Analytic Geometry, Advanced Studies in Pure Mathematics, Vol. 18-I (Academic Press, Boston, MA, 1990), pp. 327–337]. Our examples can be viewed a generalization of previous examples by Cao [Existense of gradient Kähler–Ricci solitons, in Elliptic and Parabolic Methods in Geometry (Minneapolis, MN, 1994), pp. 1–16], Chave and Valent [On a class of compact and non-compact quasi-Einstein metrics and their renormalizability properties, Nuclear Phys. B 478 (1996) 758–778], Pedersen, Tønnesen-Friedman, and Valent [Quasi-Einstein Kähler metrics, Lett. Math. Phys. 50(3) (1999) 229–241], and Feldman, Ilmanen and Knopf [Rotationally symmetric shrinking and expanding gradient Kähler–Ricci solitons, J. Differential Geom. 65 (2003) 169–209]. We also prove a uniformization result on complete steady gradient Kähler–Ricci solitons with non-negative Ricci curvature under additional assumptions.
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Yau, Shing-Tung. "Existence of canonical metrics in non-Kähler geometry." Notices of the International Congress of Chinese Mathematicians 9, no. 1 (2021): 1–10. http://dx.doi.org/10.4310/iccm.2021.v9.n1.a1.

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Dissertations / Theses on the topic "Non-Kähler geometry"

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Lee, Hwasung. "Strominger's system on non-Kähler hermitian manifolds." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:d3956c4f-c262-4bbf-8451-8dac35f6abef.

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In this thesis, we investigate the Strominger system on non-Kähler manifolds. We will present a natural generalization of the Strominger system for non-Kähler hermitian manifolds M with c₁(M) = 0. These manifolds are more general than balanced hermitian manifolds with holomorphically trivial canonical bundles. We will then consider explicit examples when M can be realized as a principal torus fibration over a Kähler surface S. We will solve the Strominger system on such construction which also includes manifolds of topology (k−1)(S²×S⁴)#k(S³×S³). We will investigate the anomaly cancellation condition on the principal torus fibration M. The anomaly cancellation condition reduces to a complex Monge-Ampère-type PDE, and we will prove existence of solution following Yau’s proof of the Calabi-conjecture [Yau78], and Fu and Yau’s analysis [FY08]. Finally, we will discuss the physical aspects of our work. We will discuss the Strominger system using α'-expansion and present a solution up to (α')¹-order. In the α'-expansion approach on a principal torus fibration, we will show that solving the anomaly cancellation condition in topology is necessary and sufficient to solving it analytically. We will discuss the potential problems with α'-expansion approach and consider the full Strominger system with the Hull connection. We will show that the α'-expansion does not correctly capture the behaviour of the solution even up to (α')¹-order and should be used with caution.
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Proto, Yann. "Geometry of heterotic flux compactifications." Electronic Thesis or Diss., Sorbonne université, 2024. http://www.theses.fr/2024SORUS125.

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Cette thèse explore des développements récents dans l'étude des compactifications avec flux de la théorie des cordes hétérotique. Nous nous concentrons principalement sur les compactifications Minkowski en quatre dimensions avec supersymétrie d'espace-temps, dont les géométries six-dimensionnelles sous-jacentes sont, en présence de torsion, des variétés non-kählériennes à structure SU(3). Nous développons plusieurs méthodes pour analyser ces compactifications à la fois du point de vue de la supergravité et de la surface d'univers. Nous étudions des flots en géométrie non-kählérienne qui jouent un rôle central dans l'étude des équations de Hull-Strominger, et élucidons leurs propriétés de supersymétrie. Nous présentons une classe d'orbifolds qui admettent une description en termes de modèles sigma linéaires avec torsion à supersymétrie (0,2), et obtenons de nouveaux exemples de fonds hétérotiques avec flux. Enfin, nous explorons les implications de la T-dualité de Narain dans l'espace des modules des vides hétérotiques avec torsion, et trouvons des preuves de changement de topologie et de dualités Kähler/non-Kähler
This thesis delves into recent developments in the study of flux compactifications of the heterotic string theory. We primarily focus on four-dimensional Minkowski compactifications with spacetime supersymmetry, whose underlying six-dimensional geometries are, in the presence of torsion, non-Kähler SU(3) structure manifolds. We develop several methods to analyze these compactifications from both supergravity and worldsheet perspectives. We investigate geometric flows in non-Kähler geometry that play a central role in the study of the Hull-Strominger equations, and elucidate their supersymmetry properties. We present a class of orbifold backgrounds that can be described using torsional linear sigma models with (0,2) worldsheet supersymmetry, and obtain new examples of heterotic flux backgrounds. Finally, we explore the implications of Narain T-duality for the moduli space of torsional heterotic vacua, and find evidence for topology change and Kähler/non-Kähler dualities
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Göteman, Malin. "The Complex World of Superstrings : On Semichiral Sigma Models and N=(4,4) Supersymmetry." Doctoral thesis, Uppsala universitet, Teoretisk fysik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-183407.

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Non-linear sigma models with extended supersymmetry have constrained target space geometries, and can serve as effective tools for investigating and constructing new geometries. Analyzing the geometrical and topological properties of sigma models is necessary to understand the underlying structures of string theory. The most general two-dimensional sigma model with manifest N=(2,2) supersymmetry can be parametrized by chiral, twisted chiral and semichiral superfields. In the research presented in this thesis, N=(4,4) (twisted) supersymmetry is constructed for a semichiral sigma model. It is found that the model can only have additional supersymmetry off-shell if the target space has a dimension larger than four. For four-dimensional target manifolds, supersymmetry can be introduced on-shell, leading to a hyperkähler manifold, or pseudo-supersymmetry can be imposed off-shell, implying a target space which is neutral hyperkähler. Different sigma models and corresponding geometries can be related to each other by T-duality, obtained by gauging isometries of the Lagrangian. The semichiral vector multiplet and the large vector multiplet are needed for gauging isometries mixing semichiral superfields, and chiral and twisted chiral superfields, respectively. We find transformations that close off-shell to a N=(4,4) supersymmetry on the field strengths and gauge potentials of the semichiral vector multiplet, and show that this is not possible for the large vector multiplet. A sigma model parametrized by chiral and twisted chiral superfields can be related to a semichiral sigma model by T-duality. The N=(4,4) supersymmetry transformations of the former model are linear and close off-shell, whereas those of the latter are non-linear and close only on-shell. We show that this discrepancy can be understood from T-duality, and find the origin of the non-linear terms in the transformations.
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Battisti, Laurent. "Variétés toriques à éventail infini et construction de nouvelles variétés complexes compactes : quotients de groupes de Lie complexes et discrets." Thesis, Aix-Marseille, 2012. http://www.theses.fr/2012AIXM4714/document.

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L'objet de cette thèse est l'étude de certaines classes de variétés complexes compactes non kählériennes. On regarde d'abord la classe des surfaces de Kato. Étant donnés une surface de Kato minimale S, D le diviseur maximal de S formé des courbes rationnelles de S et ϖ : Š ͢ S le revêtement universel de S, on démontre que Š \ϖ-1 (D) est une variété de Stein. Les variétés LVMB sont la seconde classe de variétés non kählériennes étudiées. Ces variétés complexes sont obtenues en quotientant un ouvert U de Pn par un sous-groupe de Lie fermé G de (C*)n de dimension m. On reformule ce procédé en remplaçant U par la donnée d'un sous-éventail de celui de Pn et G par un sous-espace vectoriel de Rn convenable. On construit ensuite de nouvelles variétés complexes compactes non kählériennes en combinant une méthode due à Sankaran et celle donnant les variétés LVMB. Sankaran considère un ouvert U d'une variété torique dont le quotient par un groupe W discret est une variété compacte. Ici, on munit une certaine variété torique Y de l'action d'un sous-groupe de Lie G de (C*)n de sorte que le quotient X de Y par G soit une variété, puis on quotiente un ouvert de X par un groupe discret W analogue à celui de Sankaran.Enfin, on étudie les variétés OT, une autre classe de variétés non kählériennes, dont on démontre que leur dimension algébrique est nulle. Ces variétés sont obtenues comme quotient d'un ouvert de Cm par le produit semi-direct du réseau des entiers d'une extension de corps finie K de Q et d'un sous-groupe des unités de K bien choisi
In this thesis we study certain classes of complex compact non-Kähler manifolds. We first look at the class of Kato surfaces. Given a minimal Kato surface S, D the divisor consisting of all rational curves of S and ϖ : Š ͢ S the universal covering of S, we show that Š \ϖ-1 (D) is a Stein manifold. LVMB manifolds are the second class of non-Kähler manifolds that we study here. These complex compact manifolds are obtained as quotient of an open subset U of Pn by a closed Lie subgroup G of (C*)n of dimension m. We reformulate this procedure by replacing U by the choice of a subfan of the fan of Pn and G by a suitable vector subspace of R^{n}. We then build new complex compact non Kähler manifolds by combining a method of Sankaran and the one giving LVMB manifolds. Sankaran considers an open subset U of a toric manifold whose quotient by a discrete group W is a compact manifold. Here, we endow some toric manifold Y with the action of a Lie subgroup G of (C^{*})^{n} such that the quotient X of Y by G is a manifold, and we take the quotient of an open subset of X by a discrete group W similar to Sankaran's one.Finally, we consider OT manifolds, another class of non-Kähler manifolds, and we show that their algebraic dimension is 0. These manifolds are obtained as quotient of an open subset of C^{m} by the semi-direct product of the lattice of integers of a finite field extension K over Q and a subgroup of units of K well-chosen
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Knauf, Anke [Verfasser]. "Geometric transitions on non-Kähler manifolds / vorgelegt von Anke Knauf." 2006. http://d-nb.info/979527503/34.

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Books on the topic "Non-Kähler geometry"

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Dinew, Sławomir, Sebastien Picard, Andrei Teleman, and Alberto Verjovsky. Complex Non-Kähler Geometry. Edited by Daniele Angella, Leandro Arosio, and Eleonora Di Nezza. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-25883-2.

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Angella, Daniele. Cohomological Aspects in Complex Non-Kähler Geometry. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02441-7.

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Angella, Daniele. Cohomological Aspects in Complex Non-Kähler Geometry. Springer London, Limited, 2013.

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Angella, Daniele, Sławomir Dinew, Sebastien Picard, Andrei Teleman, Alberto Verjovsky, Leandro Arosio, and Eleonora Di Nezza. Complex Non-Kähler Geometry: Cetraro, Italy 2018. Springer, 2019.

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Book chapters on the topic "Non-Kähler geometry"

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Dinew, Sławomir. "Lectures on Pluripotential Theory on Compact Hermitian Manifolds." In Complex Non-Kähler Geometry, 1–56. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-25883-2_1.

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Picard, Sébastien. "Calabi–Yau Manifolds with Torsion and Geometric Flows." In Complex Non-Kähler Geometry, 57–120. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-25883-2_2.

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Teleman, Andrei. "Non-Kählerian Compact Complex Surfaces." In Complex Non-Kähler Geometry, 121–61. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-25883-2_3.

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Verjovsky, Alberto. "Intersection of Quadrics in ℂ n $$\mathbb {C}^n$$ , Moment-Angle Manifolds, Complex Manifolds and Convex Polytopes." In Complex Non-Kähler Geometry, 163–240. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-25883-2_4.

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Tian, Gang. "Kähler-Einstein metrics with non-positive scalar curvature." In Canonical Metrics in Kähler Geometry, 43–56. Basel: Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-8389-4_5.

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Angella, Daniele. "Preliminaries on (Almost-)Complex Manifolds." In Cohomological Aspects in Complex Non-Kähler Geometry, 1–63. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-02441-7_1.

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Angella, Daniele. "Cohomology of Complex Manifolds." In Cohomological Aspects in Complex Non-Kähler Geometry, 65–94. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-02441-7_2.

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Angella, Daniele. "Cohomology of Nilmanifolds." In Cohomological Aspects in Complex Non-Kähler Geometry, 95–150. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-02441-7_3.

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Angella, Daniele. "Cohomology of Almost-Complex Manifolds." In Cohomological Aspects in Complex Non-Kähler Geometry, 151–232. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-02441-7_4.

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Liu, Xu. "Compact Smooth but Non-complex Complements of Complete Kähler Manifolds." In Complex Analysis and Geometry, 235–39. Tokyo: Springer Japan, 2015. http://dx.doi.org/10.1007/978-4-431-55744-9_17.

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