Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Complex Manifolds

Ed. by Fino, Anna Maria

Covered by Web of Science - Emerging Sources Citation Index and Zentralblatt Math (zbMATH)

CiteScore 2018: 0.64

SCImago Journal Rank (SJR) 2018: 0.643
Source Normalized Impact per Paper (SNIP) 2018: 0.812

Mathematical Citation Quotient (MCQ) 2018: 0.61

Open Access
See all formats and pricing
More options …

Some relations between Hodge numbers and invariant complex structures on compact nilmanifolds

Takumi Yamada
Published Online: 2017-06-14 | DOI: https://doi.org/10.1515/coma-2017-0006


Let N be a simply connected real nilpotent Lie group, n its Lie algebra, and € a lattice in N. If a left-invariant complex structure on N is Γ-rational, then HƏ̄s,t(Γ/N) ≃ HƏ̄s,t(nC) for each s; t. We can construct different left-invariant complex structures on one nilpotent Lie group by using the complexification and the scalar restriction. We investigate relationships to Hodge numbers of associated compact complex nilmanifolds.

Keywords : Nilmanifold; Dolbeault cohomology group; Complex structure

MSC 2010: 53C30; 22E25


  • [1] Console, S. and Fino, A.: Dolbeault cohomology of compact nilmanifolds, Transform. Groups 6 (2001), 111-124Google Scholar

  • [2] Nakamura, I.: Complex parallelisable manifolds and their small deformations, J. Differential Geom. 10 (1975), 85-112Google Scholar

  • [3] Raghunathan, M.S.: Discrete subgroups of Lie groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 68, Springer-Verlag, New York-Heidelberg, ix+227 pp. (1972)Google Scholar

  • [4] Rollenske, S.: Lie-algebra Dolbeault-cohomology and small deformations of nilmanifolds, J. Lond. Math. Soc. 79 (2009), 346-362CrossrefGoogle Scholar

  • [5] Sakane, Y.: On compact complex parallelisable solvmanifolds, Osaka J. Math. 13 (1976), 187-212Google Scholar

  • [6] Salamon, S.M.: Complex structures on nilpotent Lie algebras, J. Pure. Appl. Algebra 157 (2001), 311-333Google Scholar

  • [7] Yamada, T.: Duality of Hodge numbers of compact complex nilmanifolds, Complex manifolds 2 (2015), 168-177Google Scholar

  • [8] Yamada, T.: Hodge numbers and invariant complex structures of compact nilmanifolds, Complex manifolds 3 (2016), 193-206Google Scholar

  • [9] Yamada, T.: Remarks on Hodge numbers and invariant complex structures of compact nilmanifolds, Complex manifolds 3 (2016), 271-281Google Scholar

About the article

Received: 2017-03-10

Accepted: 2017-05-25

Published Online: 2017-06-14

Published in Print: 2017-02-23

Citation Information: Complex Manifolds, Volume 4, Issue 1, Pages 73–83, ISSN (Online) 2300-7443, DOI: https://doi.org/10.1515/coma-2017-0006.

Export Citation

© 2017. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

Comments (0)

Please log in or register to comment.
Log in