scholarly journals Homogeneous Kähler and Sasakian structures related to complex hyperbolic spaces

2010 ◽  
Vol 53 (2) ◽  
pp. 393-413 ◽  
Author(s):  
P. M. Gadea ◽  
J. A. Oubiña
Keyword(s):  
Line Bundle ◽  
Symmetric Space ◽  
Hyperbolic Space ◽  
Hermitian Symmetric Space ◽  
Complex Hyperbolic Space ◽  
Hyperbolic Spaces ◽  
Principal Line ◽  
Sasakian Structures ◽  
Kähler Structures ◽  
Complex Hyperbolic Spaces

AbstractWe study homogeneous Kähler structures on a non-compact Hermitian symmetric space and their lifts to homogeneous Sasakian structures on the total space of a principal line bundle over it, and we analyse the case of the complex hyperbolic space.

scholarly journals Incidence Axioms for the Boundary at Infinity of Complex Hyperbolic Spaces

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Sergei Buyalo ◽  
Viktor Schroeder
Keyword(s):  
Hyperbolic Space ◽  
Complex Hyperbolic Space ◽  
Hyperbolic Spaces ◽  
Complex Hyperbolic Spaces

Abstract We characterize the boundary at infinity of a complex hyperbolic space as a compact Ptolemy space that satisfies four incidence axioms.

scholarly journals DISCRETENESS CRITERIA FOR ISOMETRIC GROUPS ACTING ON COMPLEX HYPERBOLIC SPACES

2010 ◽  
Vol 81 (3) ◽  
pp. 481-487
Author(s):  
XI FU
Keyword(s):  
Hyperbolic Space ◽  
Complex Hyperbolic Space ◽  
Hyperbolic Spaces ◽  
Discreteness Criteria ◽  
Condition C ◽  
Dense Subgroups ◽  
Complex Hyperbolic Spaces ◽  
Möbius Groups

AbstractIn this paper, four new discreteness criteria for isometric groups on complex hyperbolic spaces are proved, one of which shows that the Condition C hypothesis in Cao [‘Discrete and dense subgroups acting on complex hyperbolic space’, Bull. Aust. Math. Soc.78 (2008), 211–224, Theorem 1.4] is removable; another shows that the parabolic condition hypothesis in Li and Wang [‘Discreteness criteria for Möbius groups acting on $\overline {\mathbb {R}}^n$ II’, Bull. Aust. Math. Soc.80 (2009), 275–290, Theorem 3.1] is not necessary.

scholarly journals Distribution of length spectrum of circles on a complex hyperbolic space

1999 ◽  
Vol 153 ◽  
pp. 119-140 ◽  
Author(s):  
Toshiaki Adachi
Keyword(s):  
Symmetric Space ◽  
Hyperbolic Space ◽  
Real Line ◽  
Isometry Group ◽  
Space Form ◽  
Geodesic Curvature ◽  
Real Space ◽  
Complex Hyperbolic Space ◽  
Riemannian Symmetric Space ◽  
Rank One

AbstractIt is well-known that all geodesics on a Riemannian symmetric space of rank one are congruent each other under the action of isometry group. Being concerned with circles, we also know that two closed circles in a real space form are congruent if and only if they have the same length. In this paper we study how prime periods of circles on a complex hyperbolic space are distributed on a real line and show that even if two circles have the same length and the same geodesic curvature they are not necessarily congruent each other.

Convergence theorems for total asymptotically nonexpansive single-valued and quasi nonexpansive multi-valued mappings in hyperbolic spaces

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Preeyalak Chuadchawna ◽  
Ali Farajzadeh ◽  
Anchalee Kaewcharoen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Hyperbolic Space ◽  
Hyperbolic Spaces ◽  
Iterative Sequence ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive ◽  
Uniformly Convex Hyperbolic Space

Abstract In this paper, we discuss the Δ-convergence and strong convergence for the iterative sequence generated by the proposed scheme to approximate a common fixed point of a total asymptotically nonexpansive single-valued mapping and a quasi nonexpansive multi-valued mapping in a complete uniformly convex hyperbolic space. Finally, by giving an example, we illustrate our result.

scholarly journals Integrable systems with unitary invariance from non-stretching geometric curve flows in the Hermitian symmetric space Sp(n)/U(n)

2015 ◽  
Vol 38 ◽  
pp. 1560071 ◽  
Author(s):  
Stephen C. Anco ◽  
Esmaeel Asadi ◽  
Asieh Dogonchi
Keyword(s):  
Symmetric Space ◽  
Integrable Systems ◽  
Hermitian Symmetric Space ◽  
Complex Matrix ◽  
Curve Flows ◽  
Frame Method ◽  
Parallel Frame ◽  
Natural Way ◽  
Sg Equation ◽  
Unitary Invariance

A moving parallel frame method is applied to geometric non-stretching curve flows in the Hermitian symmetric space Sp(n)/U(n) to derive new integrable systems with unitary invariance. These systems consist of a bi-Hamiltonian modified Korteweg-de Vries equation and a Hamiltonian sine-Gordon (SG) equation, involving a scalar variable coupled to a complex vector variable. The Hermitian structure of the symmetric space Sp(n)/U(n) is used in a natural way from the beginning in formulating a complex matrix representation of the tangent space 𝔰𝔭(n)/𝔲(n) and its bracket relations within the symmetric Lie algebra (𝔲(n), 𝔰𝔭(n)).

scholarly journals Hermitian symmetric space, flat bundle and holomorphicity criterion

2016 ◽  
Vol 140 (4) ◽  
pp. 1-10
Author(s):  
Hassan Azad ◽  
Indranil Biswas ◽  
C.S. Rajan ◽  
Shehryar Sikander
Keyword(s):  
Symmetric Space ◽  
Hermitian Symmetric Space ◽  
Flat Bundle
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