On the stability of invariant almost complex structures on flag manifolds

2021 ◽  
pp. 104264
Author(s):  
Francisco V. Oliveira
Keyword(s):  
Flag Manifolds ◽  
Complex Structures ◽  
Almost Complex Structures ◽  
Almost Complex ◽  
The Stability

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).

scholarly journals Invariant almost complex structures on real flag manifolds

2018 ◽  
Vol 197 (6) ◽  
pp. 1821-1844
Author(s):  
Ana P. C. Freitas ◽  
Viviana del Barco ◽  
Luiz A. B. San Martin
Keyword(s):  
Flag Manifolds ◽  
Complex Structures ◽  
Almost Complex Structures ◽  
Almost Complex

scholarly journals The complex geometry of two exceptional flag manifolds

2020 ◽  
Vol 199 (6) ◽  
pp. 2227-2241
Author(s):  
D. Kotschick ◽  
D. K. Thung
Keyword(s):  
Lie Group ◽  
Complex Geometry ◽  
Complex Structure ◽  
The Other ◽  
Flag Manifolds ◽  
Dimensional Sphere ◽  
Complex Structures ◽  
Almost Complex Structures ◽  
Almost Complex ◽  
Chern Numbers

Abstract We discuss the complex geometry of two complex five-dimensional Kähler manifolds which are homogeneous under the exceptional Lie group $$G_2$$ G 2 . For one of these manifolds, rigidity of the complex structure among all Kählerian complex structures was proved by Brieskorn; for the other one, we prove it here. We relate the Kähler assumption in Brieskorn’s theorem to the question of existence of a complex structure on the six-dimensional sphere, and we compute the Chern numbers of all $$G_2$$ G 2 -invariant almost complex structures on these manifolds.

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