Relevant bibliographies by topics / Complex hyperbolic space

Contents

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

Academic literature on the topic 'Complex hyperbolic space'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2023

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Journal articles on the topic "Complex hyperbolic space"

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Kaliman, Shulim, and Mikhail Zaidenberg. "Non-hyperbolic complex space with a hyperbolic normalization." Proceedings of the American Mathematical Society 129, no. 5 (October 20, 2000): 1391–93. http://dx.doi.org/10.1090/s0002-9939-00-05711-7.

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THAI, DO DUC, and PHAM VIET DUC. "THE KOBAYASHI k-METRICS ON COMPLEX SPACES." International Journal of Mathematics 10, no. 07 (November 1999): 917–24. http://dx.doi.org/10.1142/s0129167x99000392.

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In this article we are going to give a characterization of the hyperbolicity of complex spaces through the Kobayashi k-metrics on complex spaces and to give an integrated representation of the Kobayashi pseudo-distance on any complex space. Moreover, it is shown that a complex space is hyperbolic iff every irreducible branch of this space is hyperbolic.
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PARKER, JOHN R. "SHIMIZU’S LEMMA FOR COMPLEX HYPERBOLIC SPACE." International Journal of Mathematics 03, no. 02 (April 1992): 291–308. http://dx.doi.org/10.1142/s0129167x92000096.

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Shimizu’s lemma gives a necessary condition for a discrete group of isometries of the hyperbolic plane containing a parabolic map to be discrete. Viewing the hyperbolic plane as complex hyperbolic 1-space we generalise Shimizu’s lemma to higher dimensional complex hyperbolic space In particular we give a version of Shimizu’s lemma for subgroups of PU (n, 1) containing a vertical translation Partial generalisation to groups containing either an ellipto-parabolic map or non-vertical translations are also given together with examples that show full generalisation is not possible in these cases
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Khalfallah, Adel. "The moduli space of hyperbolic compact complex spaces." Mathematische Zeitschrift 255, no. 4 (August 26, 2006): 691–702. http://dx.doi.org/10.1007/s00209-006-0036-9.

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Li, Haizhong, and Xianfeng Wang. "Isotropic Lagrangian Submanifolds in Complex Euclidean Space and Complex Hyperbolic Space." Results in Mathematics 56, no. 1-4 (October 30, 2009): 387–403. http://dx.doi.org/10.1007/s00025-009-0422-9.

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Xiao, Yingqing, and Yueping Jiang. "Complex lines in complex hyperbolic space H ℂ 2." Indian Journal of Pure and Applied Mathematics 42, no. 5 (October 2011): 279–89. http://dx.doi.org/10.1007/s13226-011-0019-3.

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Li, Haizhong, and Xianfeng Wang. "Calabi Product Lagrangian Immersions in Complex Projective Space and Complex Hyperbolic Space." Results in Mathematics 59, no. 3-4 (April 2, 2011): 453–70. http://dx.doi.org/10.1007/s00025-011-0107-z.

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Korolkova, Anna V., Migran N. Gevorkyan, and Dmitry S. Kulyabov. "Implementation of hyperbolic complex numbers in Julia language." Discrete and Continuous Models and Applied Computational Science 30, no. 4 (December 26, 2022): 318–29. http://dx.doi.org/10.22363/2658-4670-2022-30-4-318-329.

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Hyperbolic complex numbers are used in the description of hyperbolic spaces. One of the well-known examples of such spaces is the Minkowski space, which plays a leading role in the problems of the special theory of relativity and electrodynamics. However, such numbers are not very common in different programming languages. Of interest is the implementation of hyperbolic complex in scientific programming languages, in particular, in the Julia language. The Julia language is based on the concept of multiple dispatch. This concept is an extension of the concept of polymorphism for object-oriented programming languages. To implement hyperbolic complex numbers, the multiple dispatching approach of the Julia language was used. The result is a library that implements hyperbolic numbers. Based on the results of the study, we can conclude that the concept of multiple dispatching in scientific programming languages is convenient and natural.
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Chen, Bang-Yen, and Luc Vrancken. "Lagrangian submanifolds of the complex hyperbolic space." Tsukuba Journal of Mathematics 26, no. 1 (June 2002): 95–118. http://dx.doi.org/10.21099/tkbjm/1496164384.

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Vernon, Micheal H. "Contact hypersurfaces of a complex hyperbolic space." Tohoku Mathematical Journal 39, no. 2 (1987): 215–22. http://dx.doi.org/10.2748/tmj/1178228324.

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Dissertations / Theses on the topic "Complex hyperbolic space"

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Tyler, B. M. "A computational method for the construction of Siegel sets in complex hyperbolic space." Thesis, University College London (University of London), 2010. http://discovery.ucl.ac.uk/147750/.

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This thesis presents a computational method for constructing Siegel sets for the action of \Gamma = SU(n; 1;O) on HnC, where O is the ring of integers of an imaginary quadratic field with trivial class group. The thesis first presents a basic algorithm for computing Siegel sets and then considers practical improvements which can be made to this algorithm in order to decrease computation time. This improved algorithm is implemented in a C++ program called siegel, the source code for which is freely available at http://code.google.com/p/siegel/, and this program is used to compute explicit Siegel sets for the action of all applicable groups \Gamma on H2C and H3C.
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Bogdanov, Mikhail. "Triangulations de Delaunay dans des espaces de courbure constante négative." Thesis, Nice, 2013. http://www.theses.fr/2013NICE4139.

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Nous étudions les triangulations dans des espaces de courbure négative constante, en théorie et en pratique. Ce travail est motivé par des applications dans des domaines variés. Nous considérons les complexes de Delaunay et les diagrammes de Voronoï dans la boule de Poincaré, modèle conforme de l'espace hyperbolique, en dimension quelconque. Nous utilisons l'espace des sphères pour la description des algorithmes. Nous étudions aussi les questions algébriques et arithmétiques et observons que les calculs effectués sont rationnels. Les démonstrations sont basées sur des raisonnements géométriques et n'utilisent aucune formulation analytique de la distance hyperbolique. Nous présentons une implantation complète, exacte et efficace en dimension deux. Le code est développé en vue d'une intégration dans la bibliothèque CGAL, qui permettra une diffusion à un large public. Nous étudions ensuite les triangulations de Delaunay des surfaces hyperboliques fermées. Nous définissons une triangulation comme un complexe simplicial afin de permettre l'adaptation de l'algorithme incrémentiel connu pour le cas euclidien. Le cœur de l'approche consiste à montrer l'existence d'un revêtement fini dans lequel les fibres définissent toujours une triangulation de Delaunay. Nous montrons une condition suffisante sur la longueur des boucles non contractiles du revêtement. Dans le cas particulier de la surface de Bolza, nous proposons une méthode pour construire un tel revêtement, en étudiant les sous groupes distingués du groupe fuchsien définissant la surface. Nous considérons des aspects liés à l'implantation
We study triangulations of spaces of constant negative curvature -1 from both theoretical and practical points of view. This is originally motivated by applications in various fields such as geometry processing and neuro mathematics. We first consider Delaunay complexes and Voronoi diagrams in the Poincaré ball, a conformal model of the hyperbolic space, in any dimension. We use the framework of the space of spheres to give a detailed description of algorithms. We also study algebraic and arithmetic issues, observing that only rational computations are needed. All proofs are based on geometric reasoning, they do not resort to any use of the analytic formula of the hyperbolic distance. We present a complete, exact, and efficient implementation of the Delaunay complex and Voronoi diagram in the 2D hyperbolic space. The implementation is developed for future integration into the CGAL library to make it available to a broad public. Then we study the problem of computing Delaunay triangulations of closed hyperbolic surfaces. We define a triangulation as a simplicial complex, so that the general incremental algorithm for Euclidean Delaunay triangulations can be adapted. The key idea of the approach is to show the existence of a finite-sheeted covering space for which the fibers always define a Delaunay triangulation. We prove a sufficient condition on the length of the shortest non-contractible loops of the covering space. For the specific case of the Bolza surface, we propose a method to actually construct such a covering space, by studying normal subgroups of the Fuchsian group defining the surface. Implementation aspects are considered
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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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Pinoy, Alan. "Géométrie asymptotiquement hyperbolique complexe et contraintes de courbure." Thesis, Université de Montpellier (2022-….), 2022. http://www.theses.fr/2022UMONS024.

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Dans cette thèse, nous nous intéressons aux propriétés géométriques asymptotiques d'une classe de variétés kähleriennes complètes et non compactes, que l'on appelle variétés asymptotiquement localement hyperboliques complexes. On les nomme ainsi car leur géométrie locale à l'infini est modelée sur celle de l'espace hyperbolique complexe, au sens où leur courbure est asymptotique à la courbure de l'espace hyperbolique complexe.Nous montrons que sous des hypothèses naturelles de nature géométrique, cette condition de courbure assure l'existence d'une structure riche à l'infini similaire à celle de l'espace modèle : leur bord à l'infini est muni d'une structure de Cauchy-Riemann strictement pseudoconvexe
In this thesis, we investigate the asymptotic geometric properties a class of complete and non compact Kähler manifolds we call asymptotically locally complex hyperbolic manifolds.The local geometry at infinity of such a manifold is modeled on that of the complex hyperbolic space, in the sense that its curvature is asymptotic to that of the model space.Under natural geometric assumptions, we show that this constraint on the curvature ensures the existence of a rich geometry at infinity: we can endow it with a strictly pseudoconvex CR boundary at infinity
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Cuschieri, Thomas. "Complete noncompact CMC surfaces in hyperbolic 3-space." Thesis, University of Warwick, 2009. http://wrap.warwick.ac.uk/3135/.

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In this thesis we study the asymptotic Plateau problem for surfaces with constant mean curvature (CMC) in hyperbolic 3-space H3. We give a new, geometrically transparent proof of the existence of a CMC surface spanning any given Jordan curve on the sphere at infinity of H3, for mean curvature lying in the range (-1,1). Our proof does not require methods from geometric measure theory, and yields an immersed disk as solution. We then study the dependence of the solution surface on the boundary data. We view the set of H-surfaces (CMC surfaces with mean curvature equal to H) as consisting of the conformal H-harmonic maps. We therefore begin by showing smooth dependence on boundary data for H-harmonic maps (with |H| < 1) which solve a Dirichlet problem at infinity. This is achieved by showing that the linearised H-harmonic map operator is invertible as a map between appropriate function spaces. Finally we show smooth dependence on boundary data for H-surfaces which lie in a neighbourhood of the totally umbilic spherical caps {H}. This is achieved by studying the mapping properties of the so-called conformality operator. We use methods from complex geometry to show that the linearisation of this operator at a cap H is an isomorphism for all H ∈ (−1, 1).
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Pasquinelli, Irene. "Complex hyperbolic lattices and moduli spaces of flat surfaces." Thesis, Durham University, 2018. http://etheses.dur.ac.uk/12863/.

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This work studies the Deligne-Mostow lattices in PU(2,1). These were introduced by Deligne and Mostow in several works, using monodromy of hypergeometric functions. The same lattices were rediscovered by Thurston using a geometric construction, which consists of studying possible configurations of cone points on a sphere of area 1 when the cone angles are prescribed. This space has a complex hyperbolic structure and certain automorphisms of the sphere which swap pairs of cone points, generate a lattice for some choice of initial cone angles (more precisely, the Deligne-Mostow lattices). Among these, we will consider the ones in PU(2,1). We use Thurston's approach to study the metric completion of this space, which is obtained by making pairs of cone points coalesce. Following the works of Parker and Boadi-Parker, we build a polyhedron. Using the Poincaré polyhedron theorem, we prove that the polyhedron we find is indeed a fundamental domain. Moreover, we give presentations for all Deligne-Mostow lattices in PU(2,1), calculate their volumes and show that they are coherent with the known commensurability theorems.
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Bäcklund, Pierre. "Studies on boundary values of eigenfunctions on spaces of constant negative curvature." Doctoral thesis, Uppsala University, Department of Mathematics, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-8920.

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This thesis consists of two papers on the spectral geometry of locally symmetric spaces of Riemannian and Lorentzian signature. Both works are concerned with the idea of relating analysis on such spaces to structures on their boundaries.

The first paper is motivated by a conjecture of Patterson on the Selberg zeta function of Kleinian groups. We consider geometrically finite hyperbolic cylinders with non-compact Riemann surfaces of finite area as cross sections. For these cylinders, we present a detailed investigation of the Bunke-Olbrich extension operator under the assumption that the cross section of the cylinder has one cusp. We establish the meromorphic continuation of the extension of Eisenstein series and incomplete theta series through the limit set. Furthermore, we derive explicit formulas for the residues of the extension operator in terms of boundary values of automorphic eigenfunctions.

The motivation for the second paper comes from conformal geometry in Lorentzian signature. We prove the existence and uniqueness of a sequence of differential intertwining operators for spherical principal series representations, which are realized on boundaries of anti de Sitter spaces. Algebraically, these operators correspond to homomorphisms of generalized Verma modules. We relate these families to the asymptotics of eigenfunctions on anti de Sitter spaces.

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Franco, Felipe de Aguilar. "On spaces of special elliptic n-gons." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-22032019-081425/.

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We study relations between special elliptic isometries in the complex hyperbolic plane. A special elliptic isometry can be seen as a rotation around a fixed axis (a complex geodesic). Such an isometry is determined by specifying a nonisotropic point p (the polar point to the fixed axis) and a unitary complex number a, the angle of the isometry. Any relation between special elliptic isometries with rational angles gives rise to a representation H(k1;:::;kn) → PU(2;1), where H(k1;:::;kn) : = ⟨ r1; : : : ; rn ∣ rn : : : r1> = 1; rkii = 1 ⟩ and PU(2;1) stands for the group of orientation-preserving isometries of the complex hyperbolic plane. We denote by Rpα the special elliptic isometry determined by the nonisotropic point p and by the unitary complex number α. Relations of the form Rpnαn : : :Rp1α1 = 1 in PU(2;1), called special elliptic n-gons, can be modified by short relations known as bendings: given a product RqβRpα, there exists a one-parameter subgroup B : R → SU(2;1) such that B(s) is in the centralizer of Rqβ Rpα and RB(s)qβRB(s)pα = RqβRB(s)pα for every s ∈ R. Then, for each i = 1,...,n-1, we can change Rpi+1αi+1Rpiαi by RB(s)pi+1αi+1RB(s)piαi obtaining a new n-gon. We prove that the generic part of the space of pentagons with fixed angles and signs of points is connected by means of bendings. Furthermore, we describe certain length 4 relations, called f -bendings, and prove that the space of pentagons with fixed product of angles is connected by means of bendings and f -bendings.
Neste trabalho, estudamos relações entre isometrias elípticas especiais no plano hiperbólico complexo. Uma isometria elíptica especial pode ser vista como uma rotação em torno de um eixo fixo (uma geodésica complexa). Tal isometria é determinada especificando-se um ponto não-isotrópico p (o ponto polar do eixo fixo) bem como um número complexo unitário a (o ângulo da isometria). Qualquer relação entre isometrias elípticas especiais com ângulos racionais dá origem a uma representação H(k1;:::;kn) → PU(2;1), onde H(k1;:::;kn) : = ⟨ r1; : : : ; rn ∣ rn : : : r1 = 1; rkii = 1 ⟩ e PU(2;1) é o grupo de isometrias que preservam a orientação do plano hiperbólico complexo. Denotamos por Rpα a isometria elíptica especial determinada pelo ponto não-isotrópico p e pelo complexo unitário α. Relações da forma Rpnαn : : :Rp1α1 = 1 em PU(2;1), chamadas n-ágonos elípticos especiais, podem ser modificadas a partir de relações curtas conhecidas como bendings: dado um produto RqβRpα, existe um subgrupo uniparamétrico B : R → SU(2;1) tal que B(s) está no centralizador de RqβRpα e RB(s)qβRB(s)pα = RqβRpα para todo s ∈ R. Assim, para cada i = 1; : : : ;n-1, podemos mudar Rpi+1α+1Rpiαi por RB(s)pi+1α+1RB(s)piα+1RB(s)piαi obtendo um novo n-ágono. Provamos que a parte genérica do espaço de pentágonos com ângulos e sinais de pontos fixados é conexa por meio de bendings. Além disso, descrevemos certas relações de comprimento 4, os f -bendings, e provamos que o espaço de pentágonos com produto de ângulos fixado é conexo por meio de bendings e f -bendings.
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Benzerga, Mohamed. "Structures réelles sur les surfaces rationnelles." Thesis, Angers, 2016. http://www.theses.fr/2016ANGE0081.

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Le but de cette thèse est d’apporter des éléments de réponse au problème de la finitude du nombre de classes de R-isomorphisme de formes réelles d’une surface rationnelle projective complexe lisse X quelconque, i.e. du nombre de classes d’isomorphisme de R-schémas dont le complexifié est isomorphe à X. Nous étudions ce problème en termes de structures réelles (ou involutions antiholomorphes, généralisant la conjugaison complexe) sur X : l’intérêt de cette approche est qu’elle permet une réécriture du problème faisant intervenir les groupes d’automorphismes de surfaces rationnelles, à travers la cohomologie galoisienne. Grâce à des résultats récents concernant ces groupes et en nous appuyant sur de la géométrie hyperbolique et aussi dans une moindre mesure sur de la dynamique holomorphe et de la géométrie métrique, nous prouvons plusieurs résultats généraux de finitude qui dépassent largement le seul cadre des surfaces de Del Pezzo et peuvent s’appliquer à certaines surfaces rationnelles à grands groupes d’automorphismes
The aim of this PhD thesis is to give a partial answer to the finiteness problem for R-isomorphism classes of real forms of any smooth projective complex rational surface X, i.e. for the isomorphism classes of R-schemes whose complexification is isomorphic to X. We study this problem in terms of real structures (or antiholomorphic involutions, which generalize complex conjugation) on X: the advantage of this approach is that it helps us rephrasing our problem with automorphism groups of rational surfaces, via Galois cohomology. Thanks to recent results on these automorphism groups, using hyperbolic geometry and, to a lesser extent, holomorphic dynamics and metric geometry, we prove several finiteness results which go further than Del Pezzo surfaces and can apply to some rational surfaces with large automorphism groups
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Genevois, Anthony. "Cubical-like geometry of quasi-median graphs and applications to geometric group theory." Thesis, Aix-Marseille, 2017. http://www.theses.fr/2017AIXM0569/document.

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La classe des graphes quasi-médians est une généralisation des graphes médians, ou de manière équivalente, des complexes cubiques CAT(0). L'objectif de cette thèse est d'introduire ces graphes dans le monde de la théorie géométrique des groupes. Dans un premier temps, nous étendons la notion d'hyperplan définie dans les complexes cubiques CAT(0), et nous montrons que la géométrie d'un graphe quasi-médian se réduit essentiellement à la combinatoire de ses hyperplans. Dans la deuxième partie de notre texte, qui est le cœur de la thèse, nous exploitons la structure particulière des hyperplans pour démontrer des résultats de combinaison. L'idée principale est que si un groupe agit d'une bonne manière sur un graphe quasi-médian de sorte que les stabilisateurs de cliques satisfont une certaine propriété P de courbure négative ou nulle, alors le groupe tout entier doit satisfaire P également. Les propriétés que nous considérons incluent : l'hyperbolicité (éventuellement relative), les compressions lp (équivariantes), la géométrie CAT(0) et la géométrie cubique. Finalement, la troisième et dernière partie de la thèse est consacrée à l'application des critères généraux démontrés précédemment à certaines classes de groupes particulières, incluant les produits graphés, les groupes de diagrammes introduits par Guba et Sapir, certains produits en couronne, et certains graphes de groupes. Les produits graphés constituent notre application la plus naturelle, où le lien entre le groupe et son graphe quasi-médian associé est particulièrement fort et explicite; en particulier, nous sommes capables de déterminer précisément quand un produit graphé est relativement hyperbolique
The class of quasi-median graphs is a generalisation of median graphs, or equivalently of CAT(0) cube complexes. The purpose of this thesis is to introduce these graphs in geometric group theory. In the first part of our work, we extend the definition of hyperplanes from CAT(0) cube complexes, and we show that the geometry of a quasi-median graph essentially reduces to the combinatorics of its hyperplanes. In the second part, we exploit the specific structure of the hyperplanes to state combination results. The main idea is that if a group acts in a suitable way on a quasi-median graph so that clique-stabilisers satisfy some non-positively curved property P, then the whole group must satisfy P as well. The properties we are interested in are mainly (relative) hyperbolicity, (equivariant) lp-compressions, CAT(0)-ness and cubicality. In the third part, we apply our general criteria to several classes of groups, including graph products, Guba and Sapir's diagram products, some wreath products, and some graphs of groups. Graph products are our most natural examples, where the link between the group and its quasi-median graph is particularly strong and explicit; in particular, we are able to determine precisely when a graph product is relatively hyperbolic
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Books on the topic "Complex hyperbolic space"

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Hyperbolic complex spaces. Berlin: Springer, 1998.

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Kobayashi, Shoshichi. Hyperbolic Complex Spaces. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-03582-5.

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Kobayashi, Shoshichi. Hyperbolic complex spaces. Berlin: Springer, 1998.

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Lang, Serge. Introduction to complex hyperbolic spaces. New York: Springer-Verlag, 1987.

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Lang, Serge. Introduction to Complex Hyperbolic Spaces. New York, NY: Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4757-1945-1.

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Mostly surfaces. Providence, R.I: American Mathematical Society, 2011.

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Ibragimov, Zair. Topics in several complex variables: First USA-Uzbekistan Conference on Analysis and Mathematical Physics, May 20-23, 2014, California State University, Fullerton, California. Providence, Rhode Island: American Mathematical Society, 2016.

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Aravinda, C. S. Geometry, groups and dynamics: ICTS program, groups, geometry and dynamics, December 3-16, 2012, CEMS, Kumaun University, Almora, India. Providence, Rhode Island: American Mathematical Society, 2015.

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Conformal dynamics and hyperbolic geometry: A conferece in honor of Linda Keen's 70th birthday, October 22-24, 2010, Graduate School and University Center of CUNY, New York, New York. Providence, R.I: American Mathematical Society, 2010.

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Bergeron, Nicolas. Spectre automorphe des variétés hyperboliques et applications topologiques. Paris: Société mathématique de France, 2005.

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Book chapters on the topic "Complex hyperbolic space"

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Mok, Ngaiming. "On singularities of generically immersive holomorphic maps between complex hyperbolic space forms." In Complex and Differential Geometry, 323–44. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20300-8_16.

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Sun, Li-Jie. "A Note on Poincaré’s Polyhedron Theorem in Complex Hyperbolic Space." In Springer Proceedings in Mathematics & Statistics, 351–61. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-1672-2_25.

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Mok, Ngaiming. "On the Zariski Closure of a Germ of Totally Geodesic Complex Submanifold on a Subvariety of a Complex Hyperbolic Space Form of Finite Volume." In Complex Analysis, 279–300. Basel: Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0009-5_17.

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Feistauer, Miloslav, Martin Hadrava, Jaromír Horáček, and Adam Kosík. "Numerical Solution of Fluid-Structure Interaction by the Space-Time Discontinuous Galerkin Method." In Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems, 567–75. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05591-6_56.

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Mok, Ngaiming. "Projective Algebraicity of Minimal Compactifications of Complex-Hyperbolic Space Forms of Finite Volume." In Progress in Mathematics, 331–54. Boston, MA: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8277-4_14.

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Meltz, Bertrand, Stéphane Jaouen, and Frédéric Lagoutière. "An Arbitrary Space-Time High-Order Finite Volume Scheme for Gas Dynamics Equations in Curvilinear Coordinates on Polar Meshes." In Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems, 901–9. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05591-6_91.

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Dörfler, Willy, Christian Wieners, and Daniel Ziegler. "Space-Time Discontinuous Galerkin Methods for Linear Hyperbolic Systems and the Application to the Forward Problem in Seismic Imaging." In Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, 477–85. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43651-3_44.

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Lang, Serge. "Hyperbolic Imbeddings." In Introduction to Complex Hyperbolic Spaces, 31–64. New York, NY: Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4757-1945-1_3.

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Benkhaldoun, Fayssal, and Abdallah Bradji. "Note on the Convergence of a Finite Volume Scheme for a Second Order Hyperbolic Equation with a Time Delay in Any Space Dimension." In Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, 315–24. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43651-3_28.

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Lang, Serge. "Preliminaries." In Introduction to Complex Hyperbolic Spaces, 1–10. New York, NY: Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4757-1945-1_1.

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Conference papers on the topic "Complex hyperbolic space"

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KOKUBU, MASATOSHI. "HYPERBOLIC GAUSS MAPS AND PARALLEL SURFACES IN HYPERBOLIC THREE-SPACE." In Proceedings of 9th International Workshop on Complex Structures, Integrability and Vector Fields. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814277723_0016.

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Kokubu, Masatoshi. "Linear Weingarten Surfaces in Hyperbolic Three-space." In INTERNATIONAL WORKSHOP ON COMPLEX STRUCTURES, INTEGRABILITY AND VECTOR FIELDS. AIP, 2011. http://dx.doi.org/10.1063/1.3567125.

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ADACHI, TOSHIAKI. "A DISCRETE MODEL FOR KÄHLER MAGNETIC FIELDS ON A COMPLEX HYPERBOLIC SPACE." In Proceedings of 9th International Workshop on Complex Structures, Integrability and Vector Fields. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814277723_0001.

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Yuhong, Zhang, and Yu Xuegang. "Notice of Retraction: Dirac Operator of Hyperbolic Complex Space and Unitary Transformation." In 2010 2nd International Workshop on Education Technology and Computer Science (ETCS). IEEE, 2010. http://dx.doi.org/10.1109/etcs.2010.566.

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ADACHI, Toshiaki. "A DYNAMICAL SYSTEMATIC ASPECT OF HOROCYCLIC CIRCLES IN A COMPLEX HYPERBOLIC SPACE." In Proceedings of the 3rd International Colloquium on Differential Geometry and Its Related Fields. WORLD SCIENTIFIC, 2013. http://dx.doi.org/10.1142/9789814541817_0007.

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BAO, Tuya. "SASAKIAN MAGNETIC FIELDS ON HOMOGENEOUS REAL HYPERSURFACES IN A COMPLEX HYPERBOLIC SPACE." In Proceedings of the 2nd International Colloquium on Differential Geometry and Its Related Fields. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814355476_0005.

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Zhang, Chengkun, and Junbin Gao. "Hype-HAN: Hyperbolic Hierarchical Attention Network for Semantic Embedding." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/552.

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Abstract:
Hyperbolic space is a well-defined space with constant negative curvature. Recent research demonstrates its odds of capturing complex hierarchical structures with its exceptional high capacity and continuous tree-like properties. This paper bridges hyperbolic space's superiority to the power-law structure of documents by introducing a hyperbolic neural network architecture named Hyperbolic Hierarchical Attention Network (Hype-HAN). Hype-HAN defines three levels of embeddings (word/sentence/document) and two layers of hyperbolic attention mechanism (word-to-sentence/sentence-to-document) on Riemannian geometries of the Lorentz model, Klein model and Poincaré model. Situated on the evolving embedding spaces, we utilize both conventional GRUs (Gated Recurrent Units) and hyperbolic GRUs with Möbius operations. Hype-HAN is applied to large scale datasets. The empirical experiments show the effectiveness of our method.
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BAO, Tuya, and Toshiaki ADACHI. "EXTRINSIC SHAPES OF TRAJECTORIES ON REAL HYPERSURFACES OF TYPE (B) IN A COMPLEX HYPERBOLIC SPACE." In 6th International Colloquium on Differential Geometry and its Related Fields. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789811206696_0012.

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Thompson, Lonny L., and Prapot Kunthong. "Stabilized Time-Discontinuous Galerkin Methods With Applications to Structural Acoustics." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-15753.

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The time-discontinuous Galerkin (TDG) method possesses high-order accuracy and desirable C-and L-stability for second-order hyperbolic systems including structural acoustics. C- and L-stability provide asymptotic annihilation of high frequency response due to spurious resolution of small scales. These non-physical responses are due to limitations in spatial discretization level for large-complex systems. In order to retain the high-order accuracy of the parent TDG method for high temporal approximation orders within an efficient multi-pass iterative solution algorithm which maintains stability, generalized gradients of residuals of the equations of motion expressed in state-space form are added to the TDG variational formulation. The resultant algorithm is shown to belong to a family of Pade approximations for the exponential solution to the spatially discrete hyperbolic equation system. The final form of the algorithm uses only a few iteration passes to reach the order of accuracy of the parent solution. Analysis of the multi-pass algorithm shows that the first iteration pass belongs to the family of (p+1)-stage stiff accurate Singly-Diagonal-Implicit-Runge-Kutta (SDIRK) method. The methods developed can be viewed as a generalization to the SDIRK method, retaining the desirable features of efficiency and stability, now extended to high-order accuracy. An example of a transient solution to the scalar wave equation demonstrates the efficiency and accuracy of the multi-pass algorithms over standard second-order accurate single-step/single-solve (SS/SS) methods.
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HASHINAGA, Takahiro, Akira KUBO, and Hiroshi TAMARU. "SOME TOPICS OF HOMOGENEOUS SUBMANIFOLDS IN COMPLEX HYPERBOLIC SPACES." In Proceedings of the International Workshop in Honor of S Maeda's 60th Birthday. WORLD SCIENTIFIC, 2013. http://dx.doi.org/10.1142/9789814566285_0020.

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