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<p>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 [<i>J. Math. Soc. Japan</i>, <b>60</b>, No. 2, 471–493 (2008)] and Dong [<i>J. Inst. Math. Jussieu</i>, 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.</p>

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On Some Second Main Theorems for Meromorphic Mappings of Complete KäHler Manifolds with Hyperplanes and Their Applications

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • Duc Thoan Pham,
  • Thu Thuy Hoang,
  • Thu Thuy Nguyen,
  • Thi Thuy Vu

摘要

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, No. 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.