Invariant almost complex structures on real flag manifolds

Author(s)

Freitas, Ana P. C. ^[1] ; del Barco, Viviana ^{[1, 2]} ; San Martin, Luiz A. B. ^[1]

Affiliation

^[1] Univ Estadual Campinas, IMECC, Campinas, SP - Brazil

^[2] Consejo Nacl Invest Cient & Tecn, Rosario, Santa Fe - Argentina

• Document type: Journal article
• Source: Annali di Matematica Pura ed Applicata; v. 197, n. 6, p. 1821-1844, DEC 2018.
• Web of Science Citations: 0

Abstract

In this work, we study the existence of invariant almost complex structures on real flag manifolds associated to split real forms of complex simple Lie algebras. We show that, contrary to the complex case where the invariant almost complex structures are well known, some real flag manifolds do not admit such structures. We check which invariant almost complex structures are integrable and prove that only some flag manifolds of the Lie algebra C-l admit complex structures. (AU)

• FAPESP's process: 17/13725-4 - Locally conformal geometry on flag manifolds
• Grantee: Viviana Jorgelina Del Barco
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• FAPESP's process: 12/18780-0 - Geometry of control systems, dynamical and stochastics systems
• Grantee: Marco Antônio Teixeira
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 15/23896-5 - Invariant structures on real flag manifolds
• Grantee: Viviana Jorgelina Del Barco
• Support Opportunities: Scholarships in Brazil - Post-Doctoral