论文标题
普遍的RICCI流
Generalized Ricci Flow
论文作者
论文摘要
这本书介绍了普遍的Riemannian，Complex和Kähler几何形状的基本方面。这导致了经典的爱因斯坦 - 希尔伯特（Einstein-Hilbert）作用的扩展，该动作在广义的里曼尼亚语和复杂的几何形状中产生了爱因斯坦和卡拉比结构的自然扩展。将广义的RICCI流程作为构建此类指标的工具引入，并证明了RICCI流量的基本汉密尔顿/Perelman规律性理论的扩展。这些结果在广义复合几何形状的设置中进行了完善，在该几何形状的设置中，广义的RICCI流被证明可以保留各种整合性条件，采用了多形流量和广义的Kähler-Icci流。这导致全局收敛结果，并应用于复杂的几何形状。给出了T偶尔的物理观念的纯粹数学介绍，并讨论了其与广义RICCI流的关系。
This book gives an introduction to fundamental aspects of generalized Riemannian, complex, and Kähler geometry. This leads to an extension of the classical Einstein-Hilbert action, which yields natural extensions of Einstein and Calabi-Yau structures as `canonical metrics' in generalized Riemannian and complex geometry. The generalized Ricci flow is introduced as a tool for constructing such metrics, and extensions of the fundamental Hamilton/Perelman regularity theory of Ricci flow are proved. These results are refined in the setting of generalized complex geometry, where the generalized Ricci flow is shown to preserve various integrability conditions, taking the form of pluriclosed flow and generalized Kähler-Ricci flow. This leads to global convergence results, and applications to complex geometry. A purely mathematical introduction to the physical idea of T-duality is given, and a discussion of its relationship to generalized Ricci flow.
