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Orbits of Real Forms, Matsuki Duality and CR-cohomology

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Complex and Symplectic Geometry

Part of the book series: Springer INdAM Series ((SINDAMS,volume 21))

Abstract

We discuss the relationship between groups of CR cohomology of some compact homogeneous CR manifolds and the corresponding Dolbeault cohomology groups of their canonical embeddings.

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Notes

  1. 1.

    In fact, if \(\bar{Z} \in \bar{\mathfrak{v}}_{n}\), then \(\bar{Z} = -Z + (Z +\bar{ Z})\), with \(Z =\bar{\bar{ Z}} \in \mathfrak{v}_{n}\) and \(Z +\bar{ Z} \in \upkappa _{0}\). The sum is direct because \(\mathfrak{v}_{n} \cap \upkappa _{0} =\{ 0\}\).

  2. 2.

    Actually they consider a slightly less restrictive condition, which is related to a notion of weak CR-degeneracy for homogeneous CR manifolds that was introduced in [22].

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Authors and Affiliations

  1. Dipartimento di Matematica e Fisica, III Università di Roma, Largo San Leonardo Murialdo, 1, 00146, Roma, Italy

    Stefano Marini

  2. Dipartimento di Matematica, II Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133, Roma, Italy

    Mauro Nacinovich

Authors
  1. Stefano Marini
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Correspondence to Mauro Nacinovich .

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Editors and Affiliations

  1. Dipartimento di Matematica e Informatica ‘Ulisse Dini’, University of Florence, Firenze, Italy

    Daniele Angella

  2. Dipartimento di Scienze Matematiche, Fisiche e Informatiche, University of Parma, Parma, Italy

    Costantino Medori

  3. Dipartimento di Scienze Matematiche, Fisiche e Informatiche, University of Parma, Parma, Italy

    Adriano Tomassini

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Marini, S., Nacinovich, M. (2017). Orbits of Real Forms, Matsuki Duality and CR-cohomology. In: Angella, D., Medori, C., Tomassini, A. (eds) Complex and Symplectic Geometry. Springer INdAM Series, vol 21. Springer, Cham. https://doi.org/10.1007/978-3-319-62914-8_12

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