Invariant almost complex structures on real flag manifolds
Differential Geometry
2017-08-04 v1 Representation Theory
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 admit complex structures.
Cite
@article{arxiv.1708.01218,
title = {Invariant almost complex structures on real flag manifolds},
author = {Ana P. C. Freitas and Viviana del Barco and Luiz A. B. San Martin},
journal= {arXiv preprint arXiv:1708.01218},
year = {2017}
}