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.

scholarly journals Orbits of real forms in complex flag manifolds

2010 ◽  
pp. 69-109
Author(s):  
Altomani Andrea ◽  
Medori Costantino ◽  
Nacinovich Mauro
Keyword(s):  
Flag Manifolds ◽  
Complex Flag ◽  
Real Forms ◽  
Complex Flag Manifolds

scholarly journals Families of(1,2)-symplectic metrics on full flag manifolds

2002 ◽  
Vol 29 (11) ◽  
pp. 651-664 ◽  
Author(s):  
Marlio Paredes
Keyword(s):  
Flag Manifolds ◽  
Invariant Metrics ◽  
Complex Structures ◽  
Symplectic Invariant ◽  
Almost Complex Structures ◽  
Almost Complex ◽  
Complex Flag ◽  
Complex Flag Manifolds

We obtain new families of(1,2)-symplectic invariant metrics on the full complex flag manifoldsF(n). Forn≥5, we characterizen−3differentn-dimensional families of(1,2)-symplectic invariant metrics onF(n). Each of these families corresponds to a different class of nonintegrable invariant almost complex structures onF(n).

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