In this paper we prove classification results for gradient shrinking Ricci solitons under two invariant conditions, namely nonnegative orthogonal bisectional curvature and weakly PIC₁, without any curvature upper bound. New results on ancient solutions for the Ricci and Kähler-Ricci flow are obtained. Applications to Kähler manifolds with almost nonnegative orthogonal bisectional curvature are derived as consequences. The main new feature is that no curvature upper bound is assumed.

中文翻译：

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具有非负正交二等分曲率的Kähler-Ricci收缩器和古老解决方案

在本文中，我们证明了在两个不变条件（非负正交二等分曲率和弱PIC ₁）且没有任何曲率上限的两个不变条件下梯度收缩Ricci孤子的分类结果。获得有关Ricci和Kähler-Ricci流的古代解的新结果。结果就是将其应用于具有几乎非负的正交二等分曲率的Kähler流形。主要的新功能是不假定曲率上限。