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

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
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