On some second main theorems for meromorphic mappings of complete Kähler manifolds with hyperplanes and their applications

Authors

  • Duc Thoan Pham Department of Mathematics, Hanoi University of Civil Engineering, Vietnam
  • Thu Thuy Hoang Department of Mathematics, Hanoi University of Civil Engineering, Vietnam
  • Thu Thuy Nguyen Department of Mathematics, Hanoi National University of Education, Vietnam
  • Thi Thuy Vu Department of Mathematics, Hanoi University of Civil Engineering, Vietnam

DOI:

https://doi.org/10.3842/umzh.v77i8.8785

Keywords:

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Abstract

UDC 514.7

We establish the second main theorems for meromorphic mappings of complete Kähler manifolds into complex projective spaces with hyperplanes in the general position.  This is a continuation of the works by Atsuji [J. Math. Soc. Japan, 60,  № 2,  471–493 (2008)] and Dong [J. Inst. Math. Jussieu, 1–29 (2022)]. We extend the results of these works to targets of higher dimension. As an application, we show that every meromorphic mapping of a complete Kähler manifold of nonpositive Ricci curvature and maximal volume growth into complex projective spaces with small growth, as compared to a half of the traceless Ricci curvature of the manifold, must be constant.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 77, No. 8, 2025.

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Published

11.09.2025

Issue

Vol. 77 No. 8 (2025)

Section

Research articles

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Copyright (c) 2025 Duc Thoan Pham, Thu Thuy Nguyen, Thi Thuy Vu

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Pham, Duc Thoan, et al. “On Some Second Main Theorems for Meromorphic Mappings of Complete Kähler Manifolds With Hyperplanes and Their Applications”. Ukrains’kyi Matematychnyi Zhurnal, vol. 77, no. 8, Sept. 2025, pp. 538–539, https://doi.org/10.3842/umzh.v77i8.8785.