Scalar curvature and rigidity of odd-dimensional complex hyperbolic spaces

1998 ◽  
Vol 312 (4) ◽  
pp. 641-657 ◽  
Author(s):  
Marc Herzlich
Keyword(s):  
Scalar Curvature ◽  
Hyperbolic Spaces ◽  
Complex Hyperbolic Spaces

Hyperbolic submanifolds with finite type hyperbolic Gauss map

2015 ◽  
Vol 26 (02) ◽  
pp. 1550014 ◽  
Author(s):  
Uğur Dursun ◽  
Rüya Yeğin
Keyword(s):  
Scalar Curvature ◽  
Finite Type ◽  
Hyperbolic Space ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Constant Scalar Curvature ◽  
Gauss Map ◽  
Hyperbolic Spaces ◽  
Nonzero Constant ◽  
Hyperbolic Gauss Map

We study submanifolds of hyperbolic spaces with finite type hyperbolic Gauss map. First, we classify the hyperbolic submanifolds with 1-type hyperbolic Gauss map. Then we prove that a non-totally umbilical hypersurface Mn with nonzero constant mean curvature in a hyperbolic space [Formula: see text] has 2-type hyperbolic Gauss map if and only if M has constant scalar curvature. We also classify surfaces with constant mean curvature in the hyperbolic space [Formula: see text] having 2-type hyperbolic Gauss map. Moreover we show that a horohypersphere in [Formula: see text] has biharmonic hyperbolic Gauss map.

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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