论文标题
部分可观测时空混沌系统的无模型预测
The generalized Kähler Calabi-Yau problem
论文作者
论文摘要
我们将卡拉比猜想的延伸到广义的kähler几何形状的设置。 We show a transgression formula for the Bismut Ricci curvature in this setting, which requires a new local Goto/Kodaira-Spencer deformation result, and use it to show that solutions of the generalized Calabi-Yau equation on compact manifolds are classically Kähler, Calabi-Yau, and furthermore unique in their generalized Kähler class.我们表明，广义的kähler-ricci流量自然适应了这种猜想，并表现出许多先验估计和单调性公式，这些公式表明全球存在和收敛。对于KählerCalabi-yau结构的广义Kähler类中的初始数据，我们证明该流量存在于全球，并收敛到这个独特的固定点。这具有理解广义kähler结构的空间的应用，并且作为特殊情况，可以在Hyperkähler歧管上产生自然类别的汉密尔顿象征性象征性的拓扑结构。在通勤型的Kähler结构的情况下，我们将全球存在和融合使用任意初始数据与Kähler的Calabi-yau指标，该数据为这些结构产生了新的$ d d^c $ lemma。
We formulate an extension of the Calabi conjecture to the setting of generalized Kähler geometry. We show a transgression formula for the Bismut Ricci curvature in this setting, which requires a new local Goto/Kodaira-Spencer deformation result, and use it to show that solutions of the generalized Calabi-Yau equation on compact manifolds are classically Kähler, Calabi-Yau, and furthermore unique in their generalized Kähler class. We show that the generalized Kähler-Ricci flow is naturally adapted to this conjecture, and exhibit a number of a priori estimates and monotonicity formulas which suggest global existence and convergence. For initial data in the generalized Kähler class of a Kähler Calabi-Yau structure we prove the flow exists globally and converges to this unique fixed point. This has applications to understanding the space of generalized Kähler structures, and as a special case yields the topological structure of natural classes of Hamiltonian symplectomorphisms on hyperKähler manifolds. In the case of commuting-type generalized Kähler structures we establish global existence and convergence with arbitrary initial data to a Kähler, Calabi-Yau metric, which yields a new $d d^c$-lemma for these structures.
