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<p>In this paper, we discuss the concept of HN-semipositive (HN-positive) vector bundle and also introduce strongly HN-semipositive vector bundle over compact complex manifold. Let <i>M</i> be a projective manifold with HN-semipositive tangent bundle. If <i>M</i> is rationally connected, we show that <i>T</i><sup>1,0</sup><i>M</i> is strongly HN-positive. We give a characterization of rationally connected compact Kähler manifolds with strongly HN-semipositive tangent bundle. In the second part, we show that a uniformly RC <i>k</i>-positivity implies mean curvature positivity.</p>

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Strongly HN-Positivity, Uniformly RC k-Positivity and Rational Connectedness

  • 期刊论文

  • 发表日期：

    2025年7月15日

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  • Yong Chen

摘要

In this paper, we discuss the concept of HN-semipositive (HN-positive) vector bundle and also introduce strongly HN-semipositive vector bundle over compact complex manifold. Let M be a projective manifold with HN-semipositive tangent bundle. If M is rationally connected, we show that T1,0M is strongly HN-positive. We give a characterization of rationally connected compact Kähler manifolds with strongly HN-semipositive tangent bundle. In the second part, we show that a uniformly RC k-positivity implies mean curvature positivity.