scholarly journals Slant submanifolds of complex projective and complex hyperbolic spaces

2000 ◽  
Vol 42 (3) ◽  
pp. 439-454 ◽  
Author(s):  
Bang-Yen Chen ◽  
Yoshihiko Tazawa
Keyword(s):  
Hyperbolic Spaces ◽  
Slant Submanifolds ◽  
Complex Hyperbolic Spaces ◽  
Complex Projective

Harmonic maps from surfaces into pseudo-Riemannian spheres and hyperbolic spaces

1983 ◽  
Vol 94 (3) ◽  
pp. 483-494 ◽  
Author(s):  
S. Erdem
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Harmonic Maps ◽  
Hyperbolic Spaces ◽  
Euclidean Sphere ◽  
Holomorphic Maps ◽  
Space Forms ◽  
Indefinite Metrics ◽  
Complex Hyperbolic Spaces ◽  
Complex Projective

In [2, 4, 5, 6, 7] Calabi, Barbosa and Chern showedthat there is a 2:1 correspondence between arbitrary pairs of full isotropic (terminology as in [8]) harmonic maps ±φ:M→S2mfrom a Riemann surface to a Euclidean sphere and full totally isotropic holomorphic maps f:M→2mfrom the surface to complex projective space. In this paper we show, very explicitly, how to construct a similar one-to-one correspondence whenS2mis replaced by some other space forms of positive and negative curvatures with their standard (indefinite) metrics obtained by restricting a standard (indefinite) bilinear form on Euclidean space to the tangent spaces. We get over a difficulty encountered by Barbosa of dealing with the zeros of a certain wedge product by a technique adapted from [8]. The case of complex projective space forms (indefinite complex projective and complex hyperbolic spaces) will be considered in a separate paper. Some further developments in classification theorems are given by Eells and Wood [8], Rawnsley[14], [15] and Erdem and Wood [10].

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 Polar actions on complex hyperbolic spaces

2017 ◽  
Vol 287 (3-4) ◽  
pp. 1183-1213 ◽  
Author(s):  
José Carlos Díaz Ramos ◽  
Miguel Domínguez Vázquez ◽  
Andreas Kollross
Keyword(s):  
Hyperbolic Spaces ◽  
Polar Actions ◽  
Complex Hyperbolic Spaces

scholarly journals Homogeneous structures on real and complex hyperbolic spaces

2009 ◽  
Vol 53 (2) ◽  
pp. 561-574 ◽  
Author(s):  
M. Castrillón López ◽  
P. M. Gadea ◽  
A. F. Swann
Keyword(s):  
Hyperbolic Spaces ◽  
Homogeneous Structures ◽  
Complex Hyperbolic Spaces
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