Abstract

In this study, we demonstrate that any solution to the Finslerian Ricci flow encountering a singularity on a compact manifold is invariably associated with an unbounded hh-curvature tensor. Furthermore, we establish the extended temporal viability of the Finslerian Ricci flow under the constraint of bounded curvature. To achieve this, we derive the evolution equation for the hh-curvature tensor and establish precise estimates for the covariant derivatives of the Cartan curvature tensor.

中文翻译：

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芬斯勒里奇流的长期存在

摘要

在这项研究中，我们证明了芬斯勒里奇流在紧流形上遇到奇点的任何解总是与无界hh曲率张量相关。此外，我们在有界曲率约束下建立了芬斯勒里奇流的扩展时间可行性。为了实现这一目标，我们推导了hh曲率张量的演化方程，并建立了嘉当曲率张量的协变导数的精确估计。