Paraholomorphic cohomology groups of hyperbolic adjoint orbits. (English) Zbl 1439.53030

Boumuki, Nobutaka; Noda, Tomonori

Tsukuba J. Math. 43, No. 2, 113-143 (2019).

Summary: 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.

MSC:

53C15	General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C30	Differential geometry of homogeneous manifolds
57T15	Homology and cohomology of homogeneous spaces of Lie groups

Keywords:

paracomplex manifold; cohomology group; semisimple Lie group; hyperbolic adjoint orbit; real flag manifold