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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

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2300-7443
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Example of a six-dimensional LCK solvmanifold

Hiroshi Sawai
Published Online: 2017-02-10 | DOI: https://doi.org/10.1515/coma-2017-0004

Abstract

The purpose of this paper is to prove that there exists a lattice on a certain solvable Lie group and construct a six-dimensional locally conformal Kähler solvmanifold with non-parallel Lee form.

Keywords: solvmanifold; locally conformal Kähler manifold

References

  • [1] A. Andrada and M. Origlia: Locally conformally Kähler structures on unimodular Lie groups, Geom. Dedicata 179 (2015), 197-216.Google Scholar

  • [2] D. Angella, M. Parton and V. Vuletescu: Rigidity of Oeljeklaus-Toma manifolds, arXiv:1610.04045 [math.DG].2016Google Scholar

  • [3] V. Apostolov, M. Bailey, G. Dloussky: From locally conformally Kähler to bi-Hermitian structures on non-Kähler complex surfaces, Math. Res. Lett. 22 (2015), no. 2, 317-336.Google Scholar

  • [4] L. Auslander: An exposition of the structure of solvmanifolds. I., Algebraic theory. Bull. Amer.Math. Soc. 79 (1973), 227-261.CrossrefGoogle Scholar

  • [5] P. Gauduchon, A. Moroianu and L. Ornea: Compact homogeneous lcK manifolds are Vaisman, Math. Ann. 361 (2015), no. 3-4, 1043-1048.Web of ScienceGoogle Scholar

  • [6] K. Hasegawa and Y. Kamishima: Compact homogeneous locally conformally Kählermanifolds, Osaka J.Math. 53 (2016), no. 3, 683-703.Google Scholar

  • [7] H. Kasuya : Vaisman metrics on solvmanifolds and Oeljeklaus-Toma manifolds, Bull. Lond. Math. Soc. 45 (2013), no. 1, 15-26.Google Scholar

  • [8] K. Oeljeklaus and M. Toma: Non-Kähler compact complex manifolds associated to number fields, Ann. Inst. Fourier (Grenoble) 55 (2005) 161-171.Google Scholar

  • [9] L. Ornea, M. Parton and V. Vuletescu: Holomorphic submersions of locally conformally Kähler manifolds, Ann. Mat. Pura Appl. (4) 193 (2014), no. 5, 1345-1351.Google Scholar

  • [10] A. Otiman: Currents on locally conformally Kähler manifolds, J. Geom. Phys. 86 (2014), 564-570.Google Scholar

  • [11] M. Parton and V. Vuletescu: Examples of non-trivial rank in locally conformal Kähler geometry, Math. Z. 270 (2012), no. 1-2, 179-187.Google Scholar

  • [12] M. S. Raghunathan: Discrete subgroup of Lie groups, Springer(1972).Google Scholar

  • [13] H. Sawai: Locally conformal Kähler structures on compact solvmanifolds Osaka J. Math. 49 (2012), no. 4, 1087-1102.Google Scholar

  • [14] F. Tricerri: Some examples of locally conformal Kähler manifolds, Rend. Sem. Math. Univ. Politec. Torino 40 (1982), no. 1, 81-92.Google Scholar

  • [15] I. Vaisman: Generalized Hopf manifolds, Geom. Dedicata 13 (1982), no. 3, 231-255.Google Scholar

  • [16] T. Yamada: A construction of lattices in splittable solvable Lie groups, Kodai Math. J. 39 (2016), no. 2, 378-388.Web of ScienceGoogle Scholar

About the article

Received: 2016-08-26

Accepted: 2017-01-22

Published Online: 2017-02-10

Published in Print: 2017-02-23


Citation Information: Complex Manifolds, Volume 4, Issue 1, Pages 37–42, ISSN (Online) 2300-7443, DOI: https://doi.org/10.1515/coma-2017-0004.

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

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