Holomorphically homogeneous CR manifolds and their model surfaces

2021 ◽  
Vol 85 (3) ◽  
Author(s):  
Mariya Aleksandrovna Stepanova
Keyword(s):  
Cr Manifolds ◽  
Model Surfaces ◽  
Homogeneous Cr Manifolds

scholarly journals Fibrations and globalizations of compact homogeneous CR-manifolds

2009 ◽  
Vol 73 (3) ◽  
pp. 501-553 ◽  
Author(s):  
B Gilligan ◽  
Alan T Huckleberry
Keyword(s):  
Cr Manifolds ◽  
Homogeneous Cr Manifolds

scholarly journals Compact homogeneous CR manifolds

2002 ◽  
Vol 12 (2) ◽  
pp. 183-201 ◽  
Author(s):  
Dmitry V. Alekseevsky ◽  
Andrea F. Spiro
Keyword(s):  
Cr Manifolds ◽  
Homogeneous Cr Manifolds

scholarly journals Compact homogeneous Leviflat CR-manifolds

2021 ◽  
Vol 7 (3) ◽  
Author(s):  
A. R. Al-Abdallah ◽  
B. Gilligan
Keyword(s):  
Projective Spaces ◽  
Cr Manifolds ◽  
Complex Projective Spaces ◽  
Cauchy Riemann ◽  
Complex Projective ◽  
Homogeneous Cr Manifolds

AbstractWe consider compact Leviflat homogeneous Cauchy–Riemann (CR) manifolds. In this setting, the Levi-foliation exists and we show that all its leaves are homogeneous and biholomorphic. We analyze separately the structure of orbits in complex projective spaces and parallelizable homogeneous CR-manifolds in our context and then combine the projective and parallelizable cases. In codimensions one and two, we also give a classification.

scholarly journals REDUCTIVE COMPACT HOMOGENEOUS CR MANIFOLDS

2013 ◽  
Vol 18 (2) ◽  
pp. 289-328 ◽  
Author(s):  
A. Altomani ◽  
C. Medori ◽  
M. Nacinovich
Keyword(s):  
Cr Manifolds ◽  
Homogeneous Cr Manifolds

scholarly journals ON HOMOGENEOUS CR MANIFOLDS AND THEIR CR ALGEBRAS

2006 ◽  
Vol 03 (05n06) ◽  
pp. 1199-1214
Author(s):  
ANDREA ALTOMANI ◽  
COSTANTINO MEDORI
Keyword(s):  
Lie Group ◽  
Levi Form ◽  
Flag Manifold ◽  
Semisimple Lie Group ◽  
Real Form ◽  
Cr Manifolds ◽  
Geometrical Properties ◽  
Homogeneous Cr Manifolds

In this paper we show some results on homogeneous CR manifolds, proved by introducing their associated CR algebras. In particular, we give different notions of nondegeneracy (generalizing the usual notion for the Levi form) which correspond to geometrical properties for the corresponding manifolds. We also give distinguished equivariant CR fibrations for homogeneous CR manifolds. In the second part of the paper we apply these results to minimal orbits for the action of a real form of a semisimple Lie group Ĝ on a flag manifold Ĝ/Q.

scholarly journals Higher order Levi forms on homogeneous CR manifolds

2021 ◽  
Author(s):  
S. Marini ◽  
C. Medori ◽  
M. Nacinovich
Keyword(s):  
Vector Bundles ◽  
Higher Order ◽  
Flag Manifolds ◽  
Cr Manifolds ◽  
Complex Flag ◽  
Real Forms ◽  
Complex Flag Manifolds ◽  
Homogeneous Cr Manifolds

AbstractWe investigate the nondegeneracy of higher order Levi forms on weakly nondegenerate homogeneous CR manifolds. Improving previous results, we prove that general orbits of real forms in complex flag manifolds have order less or equal than 3 and the compact ones less or equal 2. Finally we construct by Lie extensions weakly nondegenerate CR vector bundles with arbitrary orders of nondegeneracy.

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