For a paracomplex manifold, we construct certain cohomology groups. The main purpose of this paper is to clarify a link between such cohomology groups of hyperbolic adjoint orbits and the de Rham cohomology groups of real flag manifolds. That establishes relation between a paraholomorphic invariant and a topological invariant.
"Paraholomorphic cohomology groups of hyperbolic adjoint orbits." Tsukuba J. Math. 43 (2) 113 - 143, December 2019. https://doi.org/10.21099/tkbjm/1585706449