Relevant bibliographies by topics / Holomorphic curvature

Contents

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

Academic literature on the topic 'Holomorphic curvature'

Author: Grafiati
Published: 10 March 2023

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Journal articles on the topic "Holomorphic curvature"

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Ali, Danish, Johann Davidov, and Oleg Mushkarov. "Holomorphic curvatures of twistor spaces." International Journal of Geometric Methods in Modern Physics 11, no. 03 (March 2014): 1450022. http://dx.doi.org/10.1142/s0219887814500224.

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We study the twistor spaces of oriented Riemannian 4-manifolds as a source of almost Hermitian 6-manifolds of constant or strictly positive holomorphic, Hermitian and orthogonal bisectional curvatures. In particular, we obtain explicit formulas for these curvatures in the case when the base manifold is Einstein and self-dual, and observe that the "squashed" metric on ℂℙ3 is a non-Kähler Hermitian–Einstein metric of positive holomorphic bisectional curvature. This shows that a recent result of Kalafat and Koca [M. Kalafat and C. Koca, Einstein–Hermitian 4-manifolds of positive bisectional curvature, preprint (2012), arXiv: 1206.3941v1 [math.DG]] in dimension four cannot be extended to higher dimensions. We prove that the Hermitian bisectional curvature of a non-Kähler Hermitian manifold is never a nonzero constant which gives a partial negative answer to a question of Balas and Gauduchon [A. Balas and P. Gauduchon, Any Hermitian metric of constant non-positive (Hermitian) holomorphic sectional curvature on a compact complex surface is Kähler, Math. Z.190 (1985) 39–43]. Finally, motivated by an integrability result of Vezzoni [L. Vezzoni, On the Hermitian curvature of symplectic manifolds, Adv. Geom.7 (2007) 207–214] for almost Kähler manifolds, we study the problem when the holomorphic and the Hermitian bisectional curvatures of an almost Hermitian manifold coincide. We extend the result of Vezzoni to a more general class of almost Hermitian manifolds and describe the twistor spaces having this curvature property.
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Decu, Simona, Stefan Haesen, and Leopold Verstraelen. "Inequalities for the Casorati Curvature of Statistical Manifolds in Holomorphic Statistical Manifolds of Constant Holomorphic Curvature." Mathematics 8, no. 2 (February 14, 2020): 251. http://dx.doi.org/10.3390/math8020251.

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In this paper, we prove some inequalities in terms of the normalized δ -Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant) of statistical submanifolds in holomorphic statistical manifolds with constant holomorphic sectional curvature. Moreover, we study the equality cases of such inequalities. An example on these submanifolds is presented.
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SIDDIQUI, ALIYA NAAZ, and MOHAMMAD HASAN SHAHID. "Optimizations on Statistical Hypersurfaces with Casorati Curvatures." Kragujevac Journal of Mathematics 45, no. 03 (May 2021): 449–63. http://dx.doi.org/10.46793/kgjmat2103.449s.

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In the present paper, we study Casorati curvatures for statistical hypersurfaces. We show that the normalized scalar curvature for any real hypersurface (i.e., statistical hypersurface) of a holomorphic statistical manifold of constant holomorphic sectional curvature k is bounded above by the generalized normalized δ−Casorati curvatures and also consider the equality case of the inequality. Some immediate applications are discussed.
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Jain, Varun, Rachna Rani, Rakesh Kumar, and R. K. Nagaich. "Some characterization theorems on holomorphic sectional curvature of GCR-lightlike submanifolds." International Journal of Geometric Methods in Modern Physics 14, no. 03 (February 14, 2017): 1750034. http://dx.doi.org/10.1142/s0219887817500347.

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We obtain the expressions for sectional curvature, holomorphic sectional curvature and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite Sasakian manifold and obtain some characterization theorems on holomorphic sectional and holomorphic bisectional curvature.
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Kumar, Sangeet, Rakesh Kumar, and R. K. Nagaich. "Characterization of Holomorphic Bisectional Curvature ofGCR-Lightlike Submanifolds." Advances in Mathematical Physics 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/356263.

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We obtain the expressions for sectional curvature, holomorphic sectional curvature, and holomorphic bisectional curvature of aGCR-lightlike submanifold of an indefinite Kaehler manifold. We discuss the boundedness of holomorphic sectional curvature ofGCR-lightlike submanifolds of an indefinite complex space form. We establish a condition for aGCR-lightlike submanifold of an indefinite complex space form to be null holomorphically flat. We also obtain some characterization theorems for holomorphic sectional and holomorphic bisectional curvature.
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Sekigawa, Kouei, and Takashi Koda. "Compact Hermitian surfaces of pointwise constant holomorphic sectional curvature." Glasgow Mathematical Journal 37, no. 3 (September 1995): 343–49. http://dx.doi.org/10.1017/s0017089500031621.

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Let M = (M, J, g) be an almost Hermitian manifold and U(M)the unit tangent bundle of M. Then the holomorphic sectional curvature H = H(x) can be regarded as a differentiable function on U(M). If the function H is constant along each fibre, then M is called a space of pointwise constant holomorphic sectional curvature. Especially, if H is constant on the whole U(M), then M is called a space of constant holomorphic sectional curvature. An almost Hermitian manifold with an integrable almost complex structure is called a Hermitian manifold. A real 4-dimensional Hermitian manifold is called a Hermitian surface. Hermitian surfaces of pointwise constant holomorphic sectional curvature have been studied by several authors (cf. [2], [3], [5], [6] and so on).
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Yu, Chengjie. "A Liouville Property of Holomorphic Maps." Scientific World Journal 2013 (2013): 1–3. http://dx.doi.org/10.1155/2013/265752.

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We prove a Liouville property of holomorphic maps from a complete Kähler manifold with nonnegative holomorphic bisectional curvature to a complete simply connected Kähler manifold with a certain assumption on the sectional curvature.
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Vanithalakshmi, S. M., S. K. Narasimhamurthy, and M. K. Roopa. "On Holomorphic Curvature of Complex Finsler with special (α, β)−Metric." Journal of the Tensor Society 12, no. 01 (June 30, 2007): 33–48. http://dx.doi.org/10.56424/jts.v12i01.10593.

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The notion of the holomorphic curvature for a Complex Finsler space (M, F) is defined with respect to the Chern complex linear connection on the pull-back tangent bundle. This paper is about the fundamental metric tensor, inverse tensor and as a special approach of the pull-back bundle is devoted to obtain the Riemannian curvature and holomorphic curvature of Complex Finsler with special (α, β)-metric
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Abu-Saleem, Ahmad, A. R. Rustanov, and S. V. Kharitonova. "AXIOM OF Φ-HOLOMORPHIC (2r+1)-PLANES FOR GENERALIZED KENMOTSU MANIFOLDS." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 66 (2020): 5–23. http://dx.doi.org/10.17223/19988621/66/1.

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In this paper we study generalized Kenmotsu manifolds (shortly, a GK-manifold) that satisfy the axiom of Φ-holomorphic (2r+1)-planes. After the preliminaries we give the definition of generalized Kenmotsu manifolds and the full structural equation group. Next, we define Φ- holomorphic generalized Kenmotsu manifolds and Φ-paracontact generalized Kenmotsu manifold give a local characteristic of this subclasses. The Φ-holomorphic generalized Kenmotsu manifold coincides with the class of almost contact metric manifolds obtained from closely cosymplectic manifolds by a canonical concircular transformation of nearly cosymplectic structure. A Φ- paracontact generalized Kenmotsu manifold is a special generalized Kenmotsu manifold of the second kind. An analytical expression is obtained for the tensor of Ф-holomorphic sectional curvature of generalized Kenmotsu manifolds of the pointwise constant Φ-holomorphic sectional curvature. Then we study the axiom of Φ-holomorphic (2r+1)-planes for generalized Kenmotsu manifolds and propose a complete classification of simply connected generalized Kenmotsu manifolds satisfying the axiom of Φ-holomorphic (2r+1)-planes. The main results are as follows. A simply connected GK-manifold of pointwise constant Φ-holomorphic sectional curvature satisfying the axiom of Φ-holomorphic (2r+1)-planes is a Kenmotsu manifold. A GK-manifold satisfies the axiom of Φ-holomorphic (2r+1)-planes if and only if it is canonically concircular to one of the following manifolds: (1) CPn×R; (2) Cn×R; and (3) CHn×R having the canonical cosymplectic structure.
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Druţă-Romaniuc, S. L. "A Study on the Para-Holomorphic Sectional Curvature of Para-Kähler Cotangent Bundles." Annals of the Alexandru Ioan Cuza University - Mathematics 61, no. 1 (January 1, 2015): 253–62. http://dx.doi.org/10.2478/aicu-2014-0033.

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Abstract We obtain the conditions under which the total space T *M of the cotangent bundle, endowed with a natural diagonal para-Kähler structure (G, P), has constant para-holomorphic sectional curvature. Moreover we prove that (T *M,G, P) cannot have nonzero constant para-holomorphic sectional curvature.
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Dissertations / Theses on the topic "Holomorphic curvature"

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Carneiro, Josà Loester SÃ. "Sobre subvariedades totalmente reais." Universidade Federal do CearÃ, 2011. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=6646.

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Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico
CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior
Subvariedades analÃticas complexas e totalmente reais sÃo duas classes tÃpicas dentre todas as subvariedades de uma variedade quase Hermitiana. Neste trabalho procuramos dar algumas caracterizaÃÃes de subvariedades totalmente reais. AlÃm disso algumas classificaÃÃes de subvariedades totalmente reais em formas espaciais complexas sÃo obtidas.
Complex analytic submanifolds and totally real submanifolds are two typical classes among all submanifolds of an almost Hermitian manifolds. In this work, some characterizations of totally real submanifolds are given. Moreover some classifications of totally real submanifolds in complex space forms are obtained.
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Tsui, Ho-yu, and 徐浩宇. "Families of polarized abelian varieties and a construction of Kähler metrics of negative holomorphic bisectional curvature on Kodairasurfaces." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2006. http://hub.hku.hk/bib/B37053760.

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Tsui, Ho-yu. "Families of polarized abelian varieties and a construction of Kähler metrics of negative holomorphic bisectional curvature on Kodaira surfaces." Click to view the E-thesis via HKUTO, 2006. http://sunzi.lib.hku.hk/hkuto/record/B37053760.

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Santos, Adina Rocha dos. "Teoremas de comparação em variedades Käler e aplicações." Universidade Federal de Alagoas, 2011. http://repositorio.ufal.br/handle/riufal/1044.

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In this work we present the proofs of the Laplacian comparison theorems for Kähler manifolds Mm of complex dimension m with holomorphic bisectional curvature bounded from below by −1, 1, and 0. The manifolds being compared are the complex hyperbolic space CHm, the complex projective space CPm, and the complex Euclidean space Cm, which holomorphic bisectional curvatures are −1, 1, and 0, respectively. Moreover, as applications of the Laplacian comparison theorems, we describe the proof of the Bishop- Gromov comparison theorem for Kähler manifolds and obtain an estimate for the first eigenvalue λ1(M) of the Laplacian operator, that is, λ1(M) ≤ m2 = λ1(CHm), and show that the volume of Kähler manifolds with holomorphic bisectional curvature bounded from below by 1 is bounded by the volume of CPm. The results cited above have been proved in 2005 by Li and Wang, in an article Comparison theorem for Kähler Manifolds and Positivity of Spectrum , published in the Journal of Differential Geometry.
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Nesta dissertação, apresentamos as demonstrações dos teoremas de comparação do Laplaciano para variedades Kähler completas Mm de dimensão complexa m com curvatura bisseccional holomorfa limitada inferiormente por −1, 1 e 0. As variedades a serem comparadas são o espaço hiperbólico complexo CHm, o espaço projetivo complexo CPm e o espaço Euclidiano complexo Cm, cujas curvaturas bisseccionais holomorfas são −1, 1 e 0, respectivamente. Além disso, como aplicação dos teoremas de comparação do Laplaciano, descrevemos a prova do Teorema de Comparação de Bishop-Gromov para variedades Kähler; obtemos uma estimativa para o primeiro autovalor λ1(M) do Laplaciano, isto é, λ1(M) ≤ m2 = λ1(CHm); e mostramos que o volume de variedades Kähler, com curvatura bisseccional limitada inferiormente por 1, é limitado pelo volume de CPm. Os resultados citados acima foram provados em 2005 por Li e Wang no artigo Comparison Theorem for Kähler Manifolds and Positivity of Spectrum , publicado no Journal of Differential Geometry.
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Gontard, Sébastien. "Courbures de métriques invariantes dans les variétés complexes non compactes." Thesis, Université Grenoble Alpes (ComUE), 2019. http://www.theses.fr/2019GREAM027/document.

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Nous étudions les relations entre des propriétés géométriques et des propriétés métriques dans les domaines de C^n.Plus précisément, nous nous intéressons au comportement des courbures bisectionnelles holomorphes de métriques de Kähler invariantes, la métrique de Bergman et la métrique de Kähler-Einstein, au voisinage du bord des domaines pseudoconvexe bornés à bord lisse.Nous prouvons qu'aux points de stricte pseudoconvexité ou tels que la fonction squeezing du domaine tend vers 1 les courbures bisectionnelles holomorphes de la métrique de Kähler-Einstein du domaine tendent vers les courbures bisectionnelles holomorphes de la métrique de Kähler-Einstein de la boule.Nous étudions également les courbures de la métrique de Kähler-Einstein et de la métrique de Bergman dans certains domaines polynomiaux (notamment les domaines tubes et les domaines de Thullen de C^2) qui servent de modèles locaux aux points du bord qui sont de type fini. A partir de ces études nous prouvons qu'en certains points du bord de domaines convexes bornés lisse de type fini dans C^2 il existe un voisinage non tangentiel tel que les courbures bisectionnelles holomorphes de la métrique de Kâhler-Einstein sont pincées négativement. Nous prouvons également que pour tout domaine pseudoconvexe borné de type fini qui est Reinhardt complet il existe un voisinage du bord relatif au domaine tel que les courbures bisectionnelles holomorphes de la métrique de Bergman sont comprises entre deux constantes strictement négatives
We study the relationships between geometric properties and metric properties of domains in C^n.More precisely, we are interested in the behavior of holomorphic bisectional curvatures of invariant Kähler metrics, namely the Bergman metric and the Kähler-Einstein metric, near the boundary of bounded pseudoconvex domains with smooth boundary.We prove that at boundary points that are either strictly pseudoconvex or such that the squeezing function of the domain tends to one the holomorphic bisectional curvatures of the Kähler-Einstein metric of the domain tends to the holomorphic bisectional curvatures of the Kähler-Einstein metric of the ball.We also study the holomorphic bisectional curvatures of the Kähler-Einstein metric and of the Bergman metric in some polynomial domains (namely tube and Thullen domains in C^2) which serve as local models at boundary point of finite type. Using these studies we prove that at certain boundary points of smoothly bounded convex domains of finite type there exists a non tangential neighbourhood such the holomorphic bisectional curvatures of the Kähler-Einstein metric are pinched between two negative constants. We also prove that for every smoothly bounded pseudoconvex complete Reinhardt domain of finite type inf C^2 there exists a neighbourhood of the boundary relative to the domain in which the holomorphic bisectional curvatures of the Bergman metric are pinched between two negative constants
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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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LOHOVE, SIMON PETER. "Holomorphic curvature of Kähler Einstein metrics on generalised flag manifolds." Doctoral thesis, 2019. http://hdl.handle.net/2158/1151431.

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We analyse the holomorphic curvature of Kähler metrics on generalised flag manifolds with respect to the question of strict positivity. The main results are twofold: Firstly, we show that most generalised flag manifolds with second betti number smaller than 3 have positive holomorphic curvature for any Kähler metric. Secondly, using fairly different techniques we obtain that every generalised flag manifold of rank four or less has positive holomorphic curvature with respect to the Kähler-Einstein metric.
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Keshari, Dinesh Kumar. "Infinitely Divisible Metrics, Curvature Inequalities And Curvature Formulae." Thesis, 2012. http://etd.iisc.ernet.in/handle/2005/2332.

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The curvature of a contraction T in the Cowen-Douglas class is bounded above by the curvature of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. In this thesis, we characterize a slightly smaller class of contractions using a stronger form of the curvature inequality. Along the way, we find conditions on the metric of the holomorphic Hermitian vector bundle E corresponding to the operator T in the Cowen-Douglas class which ensures negative definiteness of the curvature function. We obtain a generalization for commuting tuples of operators in the Cowen-Douglas class. Secondly, we obtain an explicit formula for the curvature of the jet bundle of the Hermitian holomorphic bundle E f on a planar domain Ω. Here Ef is assumed to be a pull-back of the tautological bundle on gr(n, H ) by a nondegenerate holomorphic map f :Ω →Gr (n, H ). Clearly, finding relationships amongs the complex geometric invariants inherent in the short exact sequence 0 → Jk(Ef ) → Jk+1(Ef ) →J k+1(Ef )/ Jk(Ef ) → 0 is an important problem, whereJk(Ef ) represents the k-th order jet bundle. It is known that the Chern classes of these bundles must satisfy c(Jk+1(Ef )) = c(Jk(Ef )) c(Jk+1(Ef )/ Jk(Ef )). We obtain a refinement of this formula: trace Idnxn ( KJk(Ef )) - trace Idnxn ( KJk-1(Ef ))= KJk(Ef )/ Jk-1(Ef )(z).
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Lafrance, Marie. "Solutions à courbure constante de modèles sigma supersymétriques." Thèse, 2017. http://hdl.handle.net/1866/20204.

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"Symplectic Topology and Geometric Quantum Mechanics." Doctoral diss., 2011. http://hdl.handle.net/2286/R.I.9478.

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abstract: The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle.
Dissertation/Thesis
Ph.D. Mathematics 2011
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Books on the topic "Holomorphic curvature"

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Concentration, functional inequalities, and isoperimetry: International workshop, October 29-November 1, 2009, Florida Atlantic University, Boca Raton, Florida. Providence, R.I: American Mathematical Society, 2011.

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Book chapters on the topic "Holomorphic curvature"

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Abate, Marco, and Giorgio Patrizio. "Manifolds with constant holomorphic curvature." In Finsler Metrics—A Global Approach, 127–70. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/bfb0073983.

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Mok, Ngaiming. "Compact kähler manifolds of nonnegative holomorphic bisectional curvature." In Complex Analysis and Algebraic Geometry, 90–103. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0076997.

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Boyom, Michel Nguiffo, Aliya Naaz Siddiqui, Wan Ainun Mior Othman, and Mohammad Hasan Shahid. "Classification of Totally Umbilical CR-Statistical Submanifolds in Holomorphic Statistical Manifolds with Constant Holomorphic Curvature." In Lecture Notes in Computer Science, 809–17. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-68445-1_93.

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Diverio, Simone. "Quasi-Negative Holomorphic Sectional Curvature and Ampleness of the Canonical Class." In Complex and Symplectic Geometry, 61–71. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-62914-8_5.

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Hussin, Véronique, Marie Lafrance, and İsmet Yurduşen. "Constant Curvature Holomorphic Solutions of the Supersymmetric G(2, 4) Sigma Model." In Quantum Theory and Symmetries, 91–100. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-55777-5_8.

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Taubes, Clifford Henry. "Holomorphic submanifolds, holomorphic sections and curvature." In Differential Geometry, 268–81. Oxford University Press, 2011. http://dx.doi.org/10.1093/acprof:oso/9780199605880.003.0018.

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KLINGENBERG, WILHELM. "ON COMPACT KAEHLERIAN MANIFOLDS WITH POSITIVE HOLOMORPHIC CURVATURE." In Series in Pure Mathematics, 294–300. WORLD SCIENTIFIC, 1991. http://dx.doi.org/10.1142/9789812812797_0020.

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Bulnes, Francisco. "Integral Geometry and Cohomology in Field Theory on the Space-Time as Complex Riemannian Manifold." In Advances in Complex Analysis and Applications. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.92969.

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The study of the relationships between the integration invariants and the different classes of operators, as well as of functions inside the context of the integral geometry, establishes diverse homologies in the dual space of the functions. This is given in the class of cohomology of the integral operators that give solution to certain class of differential equations in field theory inside a holomorphic context. By this way, using a cohomological theory of appropriate operators that establish equivalences among cycles and cocycles of closed submanifolds, line bundles and contours can be obtained by a cohomology of general integrals, useful in the evaluation and measurement of fields, particles, and physical interactions of diverse nature that occurs in the space-time geometry and phenomena. Some of the results applied through this study are the obtaining of solutions through orbital integrals for the tensor of curvature R μν , of Einstein’s equations, and using the imbedding of cycles in a complex Riemannian manifold through the duality: line bundles with cohomological contours and closed submanifolds with cohomological functional. Concrete results also are obtained in the determination of Cauchy type integral for the reinterpretation of vector fields.
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HSIUNG, Chuan-Chih, Wenmao YANG, and Lew FRIEDLAND. "HOLOMORPHIC SECTIONAL AND BISECTIONAL CURVATURES OF ALMOST HERMITIAN MANIFOLDS." In Selected Papers of Chuan-Chih Hsiung, 632–53. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812810618_0061.

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Conference papers on the topic "Holomorphic curvature"

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Druţă, S. L. "COTANGENT BUNDLES WITH GENERAL NATURAL KÄHLER STRUCTURES OF QUASI-CONSTANT HOLOMORPHIC SECTIONAL CURVATURES." In Proceedings of the VIII International Colloquium. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814261173_0033.

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Journal articles
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