度量曲率及其应用2：度量里奇曲率与流
Metric Curvatures and their Applications 2: Metric Ricci Curvature and Flow
摘要：
在这第二部分中，我们概述了不同的度量曲率和它们的各种应用，我们集中在里奇曲率和流动的多面体曲面和高维流形，我们主要回顾我们以前的研究这个问题上，根据沃尔德的曲率。除了我们以前的度量方法离散的里奇曲率，我们考虑另一个，Haantjes曲率的基础上，解释为一个测地曲率。我们还试图理解最近里奇曲率离散化激增背后的数学原因。此外，我们提出了另一种方法来度量的里奇曲率，福尔曼的离散化的基础上，特别是我们建议，使用我们的图形版本的福尔曼的里奇曲率。
英文摘要：
In this second part of our overview of the different metric curvatures and their various applications, we concentrate on the Ricci curvature and flow for polyhedral surfaces and higher dimensional manifolds, and we largely review our previous studies on the subject, based upon Wald's curvature. In addition to our previous metric approaches to the discretization of Ricci curvature, we consider yet another one, based on the Haantjes curvature, interpreted as a geodesic curvature. We also try to understand the mathematical reasons behind the recent proliferation of discretizations of Ricci curvature. Furthermore, we propose another approach to the metrization of Ricci curvature, based on Forman's discretization, and in particular we propose on that uses our graph version of Forman's Ricci curvature.
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