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Invariant Generalized Almost Complex Structures on Real Flag Manifolds

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Author(s):
Valencia, Fabricio ; Varea, Carlos
Total Authors: 2
Document type: Journal article
Source: JOURNAL OF GEOMETRIC ANALYSIS; v. 32, n. 12, p. 40-pg., 2022-12-01.
Abstract

We characterize those real flag manifolds that can be endowed with invariant generalized almost complex structures. We show that no GM(2)-maximal real flag manifolds admit integrable invariant generalized almost complex structures. We give a concrete description of the generalized complex geometry on the maximal real flags of type B-2, G(2), A(3), and D-l with l >= 5, where we prove that the space of invariant generalized almost complex structures under invariant B-transformations is homotopy equivalent to a torus and we classify all invariant generalized almost Hermitian structures on them. (AU)

FAPESP's process: 20/07704-7 - Morse theory on Lie groupoids and stacks
Grantee:Fabricio Valencia Quintero
Support Opportunities: Scholarships in Brazil - Doctorate
FAPESP's process: 20/12018-5 - Higher Structures in Geometry and Mathematical Physics
Grantee:Carlos Augusto Bassani Varea
Support Opportunities: Scholarships in Brazil - Post-Doctoral