Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter July 24, 2020

Uniqueness problem of meromorphic mappings of a complete Kähler manifold into a projective space

  • Ha Huong Giang EMAIL logo
From the journal Mathematica Slovaca

Abstract

In this article, we prove a new generalization of uniqueness theorems for meromorphic mappings of a complete Kähler manifold M into ℙn(ℂ) sharing hyperplanes in general position with a general condition on the intersections of the inverse images of these hyperplanes.


This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.04-2018.01.


  1. (Communicated by Stanisława Kanas)

Acknowledgement

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.04-2018.01.

References

[1] Chen, Z—Yan, Q.: Uniqueness theorem of meromorphic mappings into ℙN(ℂ) sharing 2N + 3 hyperplanes regardless of multiplicities, Internat. J. Math. 20 (2009), 717–726.10.1142/S0129167X09005492Search in Google Scholar

[2] Dethloff, G.—Tan, T. V.: Uniqueness theorems for meromorphic mappings with few hyperplanes, Bull. Sci. Math. 133 (2009), 501–514.10.1016/j.bulsci.2008.03.006Search in Google Scholar

[3] Fujimoto, H.: The uniqueness problem of meromorphic maps into the complex projective space, Nagoya Math. J. 58 (1975), 1–23.10.1017/S0027763000016676Search in Google Scholar

[4] Fujimoto, H.: Non-integrated defect relation for meromorphic maps of complete Kähler manifolds into ℙN1(ℂ) × … × ℙNk(ℂ), Japanese J. Math. 11 (1985), 233–264.10.4099/math1924.11.233Search in Google Scholar

[5] Fujimoto, H.: A unicity theorem for meromorphic maps of a complete Kähler manifold into ℙN(ℂ), Tohoku Math. J. 38(2) (1986), 327–341.10.2748/tmj/1178228497Search in Google Scholar

[6] Giang, H. H.—Quynh, L. N.—Quang, S. D.: Uniqueness theorems for meromorphic mappings sharing few hyperplanes, J. Math. Anal. Appl. 393 (2012), 445–456.10.1016/j.jmaa.2012.03.049Search in Google Scholar

[7] Quang, S. D.—An, D. P.: Second main theorem and unicity of meromorphic mappings for hypersurfaces in projective varieties., Acta Math. Vietnam. 42 (2017), 455–470.10.1007/s40306-016-0196-6Search in Google Scholar

[8] Quang, S. D.: Unicity of meromorphic mappings sharing few hyperplanes, Ann. Polon. Math. 102(3) (2011), 255–270.10.4064/ap102-3-5Search in Google Scholar

[9] Quang, S. D.: Generalization of uniqueness theorem for meromorphic mappings sharing hyperplanes, Internat. J. Math. 30(1) (2019), 1950011, 16.10.1142/S0129167X19500113Search in Google Scholar

[10] Quynh, L. N.: Uniqueness problem of meromorphic mappings from a complete Kähler manifold into a projective variety, arXiv:1610.08822v1 [math.CV].Search in Google Scholar

[11] Hayman, W. K.: Meromorphic Functions. Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964.Search in Google Scholar

[12] Karp, L.: Subharmonic functions on real and complex manifolds, Math. Z. 179 (1982), 535–554.10.1007/BF01215065Search in Google Scholar

[13] Nevanlinna, R.: Einige Eideutigkeitssätze in der Theorie der meromorphen Funktionen, Acta. Math. 48 (1926), 367–391.10.1007/BF02565342Search in Google Scholar

[14] Noguchi, J.—Ochiai, T.: Introduction to Geometric Function Theory in Several Complex Variables. Trans. Math. Monogr. 80, Amer. Math. Soc., Providence, Rhode Island, 1990.10.1090/mmono/080Search in Google Scholar

[15] Ru, M.—Sogome, S.: Non-integrated defect relation for meromorphic maps of complete K¨ahler manifold intersecting hypersurface in ℙn(C), Trans. Amer. Math. Soc. 364 (2012), 1145–1162.10.1090/S0002-9947-2011-05512-1Search in Google Scholar

[16] Smiley, L.: Geometric conditions for unicity of holomorphic curves, Contemp. Math. 25 (1983), 149–154.10.1090/conm/025/730045Search in Google Scholar

[17] Thai, D. D.—Quang, S. D.: Uniqueness problem with truncated multiplicities of meromorphic mappings in several compex variables, Internat. J. Math. 17 (2006), 1223–1257.10.1142/S0129167X06003898Search in Google Scholar

[18] Yau, S. T.: Some function-theoretic properties of complete Riemannian manifolds and their applications to geometry, Indiana Univ. Math. J. 25 (1976), 659–670.10.1512/iumj.1976.25.25051Search in Google Scholar

Received: 2019-01-03
Accepted: 2019-12-18
Published Online: 2020-07-24
Published in Print: 2020-08-26

© 2020 Mathematical Institute Slovak Academy of Sciences

Downloaded on 29.3.2024 from https://www.degruyter.com/document/doi/10.1515/ms-2017-0399/html
Scroll to top button