scholarly journals Theorems of Barth-Lefschetz type for complex subspaces of homogeneous complex manifolds

1977 ◽  
Vol 74 (4) ◽  
pp. 1332-1333 ◽  
Author(s):  
A. J. Sommese
Keyword(s):  
Complex Manifolds ◽  
Homogeneous Complex ◽  
Lefschetz Type

scholarly journals Quaternionic-like manifolds and homogeneous twistor spaces

2016 ◽  
Vol 472 (2196) ◽  
pp. 20160598
Author(s):  
Radu Pantilie
Keyword(s):  
Complex Manifolds ◽  
Twistor Spaces ◽  
Adequate Level ◽  
Homogeneous Complex ◽  
Quaternionic Manifold ◽  
Quaternionic Geometry ◽  
Real Analytic ◽  
Quaternionic Manifolds

Motivated by the quaternionic geometry corresponding to the homogeneous complex manifolds endowed with (holomorphically) embedded spheres, we introduce and initiate the study of the ‘quaternionic-like manifolds’. These contain, as particular subclasses, the CR quaternionic and the ρ -quaternionic manifolds. Moreover, the notion of ‘heaven space’ finds its adequate level of generality in this setting: (essentially) any real analytic quaternionic-like manifold admits a (germ) unique heaven space, which is a ρ -quaternionic manifold. We, also, give a natural construction of homogeneous complex manifolds endowed with embedded spheres, thus, emphasizing the abundance of the quaternionic-like manifolds.

scholarly journals On closed radical orbits in homogeneous complex manifolds

1996 ◽  
Vol 54 (3) ◽  
pp. 363-368 ◽  
Author(s):  
Bruce Gilligan
Keyword(s):  
Finite Number ◽  
Lie Group ◽  
Discrete Subgroup ◽  
Connected Components ◽  
Complex Manifolds ◽  
Algebraic Subgroup ◽  
Homogeneous Complex ◽  
Semisimple Complex ◽  
Klein Form

Suppose G is a complex Lie group having a finite number of connected components and H is a closed complex subgroup of G with H° solvable. Let RG denote the radical of G. We show the existence of closed complex subgroups I and J of G containing H such that I/H is a connected solvmanifold with I° ⊃ RG, the space G/J has a Klein form SG/A, where A is an algebraic subgroup of the semisimple complex Lie group SG: = G/RG, and, unless I = J, the space J/I has Klein form , where is a Zariski dense discrete subgroup of some connected positive dimensional semisimple complex Lie group Ŝ.

scholarly journals Locally homogeneous complex manifolds

1969 ◽  
Vol 123 (0) ◽  
pp. 253-302 ◽  
Author(s):  
Phillip Griffiths ◽  
Wilfried Schmid
Keyword(s):  
Complex Manifolds ◽  
Homogeneous Complex ◽  
Locally Homogeneous
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