Kobayashi-Hitchin correspondence for polarized algebraic manifolds and Kahler-Ricci flows

首先，我们将Kahler-Ricci孤子的概念推广到一般极化流形的情况，称为广义Kahler-Ricci孤子。此外，我们还构造了广义Kahler-Ricci孤子的一个非平凡例子。其次，我们构造了非圆Einstein-Sasaki流形的新例子，即我们在与Kahler-Einstein Fano流形上的射影线丛的典范线丛相关的某些单位圆丛上构造了Einstein-Sasaki度量

Firstly, we have generalized the notion of Kahler-Ricci solitons to the case of general polarized manifolds, which are called" generalized Kahler-Ricci solitons". Moreover, we have constructed a non-trivial example of a generalieze Kahler-Ricci soliton. Next, we have constructed new examples of non-toric Einstein-Sasaki manifolds, that is, we have constructed Einstein-Sasaki metrics on certain unit-circle bundles associated to the canonical line bundles of projective line-bundles over Kahler-Einstein Fano manifolds