第二类具有六正曲率算子的Kähler曲面
Kähler surfaces with six-positive curvature operator of the second kind
摘要：
本文的目的是开始研究Kähler流形上的第二类曲率算子。主要结果是：第二类具有六个正曲率算子的闭Kähler曲面与$\mathbb{CP}^2$是双全纯的.证明了具有第二类六个非负曲率算子的闭非平坦Kähler曲面要么与$\mathbb{CP}^2$双全纯，要么与$\mathbb{S}^2 \times \mathbb{S}^2$等距.
英文摘要：
The purpose of this article is to initiate the investigation of the curvature operator of the second kind on Kähler manifolds. The main result asserts that a closed Kähler surface with six-positive curvature operator of the second kind is biholomorphic to $\mathbb{CP}^2$. It is also shown that a closed non-flat Kähler surface with six-nonnegative curvature operator of the second kind is either biholomorphic to $\mathbb{CP}^2$ or isometric to $\mathbb{S}^2 \times \mathbb{S}^2$.
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