强hn -正性、一致RC - k-正性和有理连通性

IF 0.9 3区数学 Q2 MATHEMATICS

Acta Mathematica Sinica-English Series Pub Date : 2025-07-15 DOI:10.1007/s10114-025-3217-3

Yong Chen

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引用次数: 0

摘要

本文讨论了紧复流形上的n -半正（n -正）向量束的概念，并引入了强n -半正向量束。设M是一个具有hn -半正切束的投影流形。如果M是理性连接的，我们证明T1,0M是强hn阳性的。给出了具有强hn -半正切束的合理连通紧致Kähler流形的一个性质。在第二部分中，我们证明了一致的RC k正意味着平均曲率正。

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

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 T^1,0M 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.

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来源期刊

Acta Mathematica Sinica-English Series 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

138

审稿时长

14.5 months

期刊介绍： Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.