abstract:

In this paper we study the class of compact K\"ahler manifolds with ${\rm Ric}^\perp>0$. First we illustrate examples of K\"ahler manifolds with ${\rm Ric}^\perp>0$ on K\"ahler C-spaces, and construct ones on certain projectivized vector bundles. These examples show the abundance of K\"ahler manifolds which admit metrics of ${\rm Ric}^\perp>0$. Secondly we prove some (algebraic) geometric consequences of the condition ${\rm Ric}^\perp>0$ to illustrate that the condition is also quite restrictive. Finally this last point is made evident with a classification result in dimension three and a partial classification in dimension four.

摘要：

在本文中，我们研究了 ${\rm Ric}^\perp>0$ 的紧致 K\"ahler 流形类。首先我们举例说明 ${\rm Ric}^\perp>0 的 K\"ahler 流形$ 在 K\"ahler C 空间上，并在某些投影向量丛上构造它们。这些例子显示了 K\"ahler 流形的丰富性，它承认 ${\rm Ric}^\perp>0$ 的度量。其次，我们证明了条件 ${\rm Ric}^\perp>0$ 的一些（代数）几何结果，以说明该条件也是非常严格的。最后，这最后一点通过维度三的分类结果和维度四的部分分类变得明显。