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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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Strongly not relatives Kähler manifolds

Michela Zedda
Published Online: 2017-02-08 | DOI: https://doi.org/10.1515/coma-2017-0001

Abstract

In this paper we study Kähler manifolds that are strongly not relative to any projective Kähler manifold, i.e. those Kähler manifolds that do not share a Kähler submanifold with any projective Kähler manifold even when their metric is rescaled by the multiplication by a positive constant. We prove two results which highlight some relations between this property and the existence of a full Kähler immersion into the infinite dimensional complex projective space. As application we get that the 1-parameter families of Bergman-Hartogs and Fock-Bargmann-Hartogs domains are strongly not relative to projective Kähler manifolds.

Keywords: Kähler manifolds; complex submanifolds; diastasis function

References

  • [1] E. Bi, Z. Feng, Z. Tu, Balanced metrics on the Fock-Bargmann-Hartogs domains, Ann Glob Anal Geom 49 (2016), n. 4, 349-359.Web of ScienceGoogle Scholar

  • [2] S. Bochner, Curvature in Hermitian metric, Bull. Amer. Math. Soc. 53 (1947), 179-195.Google Scholar

  • [3] E. Calabi, Isometric imbedding of complex manifolds, Ann. of Math. (2) 58 (1953), 1-23.CrossrefGoogle Scholar

  • [4] X. Cheng, A. J. Di Scala, Y. Yuan, Kähler submanifolds and the Umehara Algebra, preprint 2016, arXiv: 1601.05907v2 [math.DG].Google Scholar

  • [5] A. J. Di Scala, H. Ishi, A. Loi, Kähler immersions of homogeneous Kähler manifolds into complex space forms, Asian J. Math. (3) 16 (2012), 479-488.Google Scholar

  • [6] A. J. Di Scala, A. Loi, Kähler manifolds and their relatives, Ann. Scuola Normale Pisa (3) 9 (2010), 495-501.Google Scholar

  • [7] Z. Feng, Z. Tu, Balanced metrics on some Hartogs type domains over bounded symmetric domains, Ann. of Glob. Anal. Geom. 47 (2015), (4), 305-333.Google Scholar

  • [8] Y. Hao, A. Wang, Kähler geometry of bounded pseudoconvex Hartogs domains, preprint 2014, arXiv:1411.4447 [math.CV].Google Scholar

  • [9] Y. Hao, A.Wang, The Bergman kernels of generalized Bergman-Hartogs domains, J.Math. Anal. Appl. 429 (2015), 1, 326-336.Google Scholar

  • [10] X. Huang, Y. Yuan, Submanifolds of Hermitian symmetric spaces, Springer Proc. Math. Stat. 127 (2015), Analysis and Geometry, Springer, 197-206.Google Scholar

  • [11] S. Kobayashi, Geometry of Bounded Domains, Trans. Amer. Math. Soc. 92 (1996), 267-290.Google Scholar

  • [12] A. Loi, R. Mossa, Berezin quantization of homogeneous bounded domains , Geom. Ded. 161 (2012), 1, 119-128.Google Scholar

  • [13] A. Loi, M. Zedda, Kähler-Einstein submanifolds of the infinite dimensional projective space,Math. Ann. 350 (2011), 145-154.Web of ScienceGoogle Scholar

  • [14] A. Loi, M. Zedda, Balanced metrics on Cartan and Cartan-Hartogs domains, Math. Zeit. 270 (3-4), 1077-1087.Google Scholar

  • [15] R. Mossa, A bounded homogeneous domain and a projective manifold are not relatives. Riv. Mat. Univ. Parma 4 (2013), (1), 55-59.Google Scholar

  • [16] M. Umehara, Kähler submanifolds of complex space forms, Tokyo J. Math. 10 (1987), 1, 203-214.Google Scholar

  • [17] M. Zedda, Berezin-Engliš’ quantization of Cartan-Hartogs domains, J. Geom. Phys. 100 (2016), 62-67.CrossrefGoogle Scholar

  • [18] J. Zhao, A.Wang, Y. Hao, On the holomorphic automorphism group of the Bergman-Hartogsdomain, Int. J.Math. (8) 26 (2015), art. n. 1550056.Google Scholar

About the article

Received: 2016-09-24

Accepted: 2016-11-06

Published Online: 2017-02-08

Published in Print: 2017-02-23


Citation Information: Complex Manifolds, Volume 4, Issue 1, Pages 1–6, ISSN (Online) 2300-7443, DOI: https://doi.org/10.1515/coma-2017-0001.

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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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