Results 21 to 30 of about 634,077 (306)

An Extension of Poincare Model of Hyperbolic Geometry with Gyrovector Space Approach [PDF]

Mathematics Interdisciplinary Research, 2016
‎The aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]‎. ‎In [1]‎, ‎Ungar and Chen showed that the algebra of the group SL(2, C) naturally leads to the notion of gyrogroups ‎and gyrovector spaces for dealing ...
Mahfouz Rostamzadeh, Sayed-Ghahreman Taherian   +1 more
doaj   +1 more source

Exponential and logarithm of multivector in low-dimensional (n = p + q < 3) Clifford algebras

Nonlinear Analysis, 2022
The aim of the paper is to give a uniform picture of complex, hyperbolic, and quaternion algebras from a perspective of the applied Clifford geometric algebra.
Adolfas Dargys, Artūras Acus
doaj   +1 more source

Community Division Algorithm by Minimum Based on Hyperbolic Space Embedding [PDF]

Jisuanji gongcheng, 2020
The distribution of real complex network nodes obeys power laws,and the hyperbolic geometry can fully represent such characteristics.On this basis,this paper proposes a community division algorithm based on hyperbolic space embedding and minumun ...
XIE Jing, YI Shuwen, ZHANG Yi
doaj   +1 more source

Projective structures, grafting, and measured laminations [PDF]

, 2007
We show that grafting any fixed hyperbolic surface defines a homeomorphism from the space of measured laminations to Teichmuller space, complementing a result of Scannell-Wolf on grafting by a fixed lamination.
Bers, Bers, Bonahon, Bonahon, Bonahon, David Dumas, Dumas, Dumas, Epstein, Epstein, Gardiner, Gardiner, Goldman, Kamishima, Katok, Kerckhoff, Levitt, Maskit, Michael Wolf, Nag, Otal, Papadopoulos, Penner, Rees, Series, Sullivan, Tanigawa, Thurston, Tromba, Zograf   +29 more
core   +3 more sources

Harmonic Analysis on Quantum Complex Hyperbolic Spaces [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2011
In this paper we obtain some results of harmonic analysis on quantum complex hyperbolic spaces. We introduce a quantum analog for the Laplace-Beltrami operator and its radial part. The latter appear to be second order $q$-difference operator, whose eigenfunctions are related to the Al-Salam-Chihara polynomials. We prove a Plancherel type theorem for it.
Bershtein, Olga, Kolisnyk, Ye.
openaire   +4 more sources

On the Hyperbolicity and the Schottky Property of Complex Spaces [PDF]

Proceedings of the American Mathematical Society, 1994
The purpose of this paper is to study the hyperbolicity and the tautness of spaces that have the Schottky property. Moreover, the hyperbolicity of compact complex spaces is characterized by the classical theorem of Bloch.
openaire   +1 more source

The homogeneous geometries of complex hyperbolic space [PDF]

, 2021
We describe the holonomy algebras of all canonical connections and their action on complex hyperbolic spaces $\mathbb{C}\mathrm{H}(n)$ in all dimensions ($n\in\mathbb{N}$). This thorough investigation yields a formula for all Kahler homogeneous structures on complex hyperbolic spaces. Finally, we have related the belonging of the homogeneous structures
Carmona Jiménez, J. L., Castrillón López, Marco   +1 more
openaire   +3 more sources

Predicting Long-term Dynamics of Complex Networks via Identifying Skeleton in Hyperbolic Space [PDF]

Knowledge Discovery and Data Mining
Learning complex network dynamics is fundamental for understanding, modeling, and controlling real-world complex systems. Though great efforts have been made to predict the future states of nodes on networks, the capability of capturing long-term ...
Ruikun Li, Huandong Wang, J. Piao, Qingmin Liao, Yong Li   +4 more
semanticscholar   +1 more source

Real reflections, commutators and cross-ratios in complex hyperbolic space [PDF]

, 2013
We provide a concrete criterion to determine whether or not two given elements of PU(2,1) can be written as products of real reflections, with one reflection in common. As an application, we show that the Picard modular groups ${\rm PU}(2,1,\mathcal{O}_d)
Julien Paupert, Pierre Will
semanticscholar   +1 more source

Minimal Lagrangian surfaces in CH^2 and representations of surface groups into SU(2,1) [PDF]

, 2012
We use an elliptic differential equation of Tzitzeica type to construct a minimal Lagrangian surface in the complex hyperbolic plane CH^2 from the data of a compact hyperbolic Riemann surface and a small holomorphic cubic differential.
Loftin, John, McIntosh, Ian
core   +1 more source