Skip to main content
SpringerLink
Log in

A Pseudo-Kähler Structure on a Nontoral Compact Complex Parallelizable Solvmanifold

  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

Abstract

In this paper, we construct a non-toral compact complex parallelizable pseudo-Kähler solvmanifold.pseudo-Kähler, complex-parallelizable manifold, compact solvmanifold, Borel–Remmert theorem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Reference

  1. L.C. Andrés Particlede M. Fernández M. León Particlede J.J. Mencía (1992) ArticleTitleSome six dimensional compact symplectic and complex solvmanifolds Rend Mat. Ser. 7 12 59–67

    Google Scholar 

  2. C. Benson C. Gordon (1990) ArticleTitleKähler structures on solvmanifolds Proc. Amer. Math. Soc. 108 971–980

    Google Scholar 

  3. A. Borel R. Remmert (1961/1962) ArticleTitleÜber kompakte homogene Kählersche mannigfaltigkeiten Math. Ann. 145 429–439 Occurrence Handle10.1007/BF01471087

    Article  Google Scholar 

  4. L.C. Cordero M. Fernández L. Ugarte (2002) ArticleTitleLefschetz complex conditions for complex manifolds Ann. Global Anal. Geom. 22 355–373 Occurrence Handle10.1023/A:1020527112556

    Article  Google Scholar 

  5. J. Dorfmeister Z.-D. Guan (1992) ArticleTitleClassification of compact homogeneous pseudo-Kähler manifolds Comment. Math. Helv. 67 499–513

    Google Scholar 

  6. Guan D., (1994) Examples of Compact Holomorphic Symplectic Manifolds which Admit no Kähler Structure. Geometry and Analysis on Complex Manifolds, World Scientific, River Edge, NJ , pp. 63–74.

  7. D. Guan (1995) ArticleTitleExamples of compact holomorphic symplectic manifolds which are not Kählerian III Internat. J. Math. 6 709–718 Occurrence Handle10.1142/S0129167X95000298

    Article  Google Scholar 

  8. D. Guan (1996) ArticleTitleA splitting theorem for compact complex homogeneous space with a symplectic structure Geom. Dedicata 63 217–225 Occurrence Handle10.1007/BF00148221

    Article  Google Scholar 

  9. A. Hattori (1960) ArticleTitleSpectral sequence in the de Rham cohomology of fibre bundles J. Fac. Sci. Univ. Tokyo, Sect. 1 IssueID8, 289–331 1–8, 289331

    Google Scholar 

  10. A. Huckleberry (1990) ArticleTitleHomogeneous pseudo-Kählerian manifolds: a Hamiltonian viewpoint Note Mat. 10 Suppl–2, 337342

    Google Scholar 

  11. Y. Matsushima (1957) ArticleTitleSur les homogénes kählériens d’un groupe de Lie réductif Nagoya Math. J. 11 53–60

    Google Scholar 

  12. I. Nakamura (1975) ArticleTitleComplex parallelisable manifolds and their small deformations J. Differential Geom. 10 85–112

    Google Scholar 

  13. K. Nomizu (1954) ArticleTitleOn the cohomology of compact homogeneous spaces of nilpotent Lie groups Ann. Math. 59 531–538

    Google Scholar 

  14. M.S. Raghunathan (1972) Discrete Subgroups of Lie Groups Springer-Verlag Berlin

    Google Scholar 

  15. M. Saitô (1957) ArticleTitleSur certains groupes de Lie résolubles Sci. Papers Coll. Gen. Ed. Univ. Tokyo 7 1–11

    Google Scholar 

  16. M. Saitô (1957) ArticleTitleSur certains groupes de Lie résolubles II Sci. Papers Coll. Gen. Ed. Univ. Tokyo 7 157–168

    Google Scholar 

  17. Y. Sakane (1976) ArticleTitleOn compact complex parallelisable solvmanifolds Osaka J. Math. 13 187–212

    Google Scholar 

  18. H.C. Wang (1954) ArticleTitleComplex parallisable manifolds Proc. Amer. Math. Soc. 5 771–776

    Google Scholar 

  19. Yamada T.,: A construction of compact pseudo-Kähler solvmanifolds with no Kähler structures, to appear in Tsukuba J. Math.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Osaka University, Japan

    Takumi Yamada

Authors
  1. Takumi Yamada
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Takumi Yamada.

Additional information

Mathematics Subject Classiffications (2000). 53C15, 53D05

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yamada, T. A Pseudo-Kähler Structure on a Nontoral Compact Complex Parallelizable Solvmanifold. Geom Dedicata 112, 115–122 (2005). https://doi.org/10.1007/s10711-004-3397-4

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10711-004-3397-4

Keywords

Search

Navigation