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<p>In this paper, we will study Kähler-Finsler manifolds with positive curvatures. We initially establish a relationship between the holomorphic bisectional curvature and horizontal flag curvature. Utilizing this observation along with the complex second variation formula, we demonstrate Myers type theorems and Frankel type intersection theorems on Kähler-Finsler manifolds. Subsequently, we present some vanishing theorems and their applications on complex Finsler manifolds. Finally, we establish the proof of the Frankel conjecture for Kähler-Finsler surfaces.</p>

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Kähler-Finsler manifolds with positive curvatures

  • 期刊论文

  • 发表日期：

    2025年1月6日

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  • Jinling Li,
  • Jintang Li,
  • Chunhui Qiu,
  • Qixin Zhang

摘要

In this paper, we will study Kähler-Finsler manifolds with positive curvatures. We initially establish a relationship between the holomorphic bisectional curvature and horizontal flag curvature. Utilizing this observation along with the complex second variation formula, we demonstrate Myers type theorems and Frankel type intersection theorems on Kähler-Finsler manifolds. Subsequently, we present some vanishing theorems and their applications on complex Finsler manifolds. Finally, we establish the proof of the Frankel conjecture for Kähler-Finsler surfaces.