The Long-Time Existence of the Finslerian Ricci Flow

IF 0.7 4区数学 Q2 MATHEMATICS

Bulletin of The Iranian Mathematical Society Pub Date : 2024-03-04 DOI:10.1007/s41980-023-00857-6

引用次数: 0

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.

查看原文本刊更多论文

芬斯勒利玛窦流的长期存在

摘要在本研究中，我们证明了在紧凑流形上遇到奇点的任何芬斯勒利玛窦流的解无一例外地与无界曲率张量相关联。此外，我们还建立了有界曲率约束下的 Finslerian Ricci 流的扩展时间可行性。为此，我们推导了 hh曲率张量的演化方程，并建立了 Cartan曲率张量协变导数的精确估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Bulletin of The Iranian Mathematical Society Mathematics-General Mathematics

CiteScore

1.40

自引率

0.00%

发文量

期刊介绍： The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.