scholarly journals Mixed foliate CR-submanifolds in a complex hyperbolic space are non-proper

1988 ◽  
Vol 11 (3) ◽  
pp. 507-515 ◽  
Author(s):  
Bang-Yen Chen ◽  
Bao-Qiang Wu
Keyword(s):  
Hyperbolic Space ◽  
Complex Hyperbolic Space ◽  
Real Submanifolds ◽  
Complex Submanifolds ◽  
Affirmative Solution ◽  
Totally Real ◽  
Cr Submanifolds

It was conjectured in [1 II] (also in [2]) that mixed foliate CR-submanifolds in a complex hyperbolic space are either complex submanifolds or totally real submanifolds. In this paper we give an affirmative solution to this conjecture.

scholarly journals Bounded cohomology and totally real subspaces in complex hyperbolic geometry

2011 ◽  
Vol 32 (2) ◽  
pp. 467-478 ◽  
Author(s):  
MARC BURGER ◽  
ALESSANDRA IOZZI
Keyword(s):  
Hyperbolic Space ◽  
Hyperbolic Geometry ◽  
Isometry Group ◽  
Complex Hyperbolic Space ◽  
Discrete Groups ◽  
Connected Component ◽  
Bounded Cohomology ◽  
Finitely Generated ◽  
Complex Hyperbolic Geometry ◽  
Totally Real

AbstractWe characterize representations of finitely generated discrete groups into (the connected component of) the isometry group of a complex hyperbolic space via the pullback of the bounded Kähler class.

Smooth Boundary Values Along Totally Real Submanifolds

1984 ◽  
Vol 36 (2) ◽  
pp. 240-248 ◽  
Author(s):  
Edgar Lee Stout
Keyword(s):  
Pseudoconvex Domain ◽  
Smooth Boundary ◽  
Regularity Result ◽  
Boundary Values ◽  
Real Submanifolds ◽  
Strongly Pseudoconvex Domain ◽  
Real Submanifold ◽  
Totally Real Submanifold ◽  
Class C ◽  
Totally Real

The main result of this paper is the following regularity result:THEOREM. Let D ⊂ CNbe a bounded, strongly pseudoconvex domain with bD of class Ck, k ≧ 3. Let Σ ⊂ bD be an N-dimensional totally real submanifold, and let f ∊ A(D) satisfy |f| = 1 on Σ, |f| < 1 on. If Σ is of class Cr, 3 ≦ r < k, then the restriction fΣ = f|Σ of f to Σ is of class Cr − 0, and if Σ is of class Ck, then fΣ is of class Ck − 1.Here, of course, A(D) denotes the usual space of functions continuous on , holomorphic on D, and we shall denote by Ak(D), k = 1, 2, …, the space of functions holomorphic on D whose derivatives or order k lie in A(D).

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