Methods of Riemannian geometry in the Finsler geometry

芬斯勒几何中黎曼几何的方法

• 批准号: 318916629
• 负责人: Professor Dr. Vladimir Matveev
• 金额: --
• 依托单位: Lehrstuhl für Differentialgeometrie
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/318916629?language=en
• 关键词: Methods; Riemannian; geometry; Finsler

Our goal is to solve the following three problems in Finlser geometry:Problem 1 (Landsberg Unicorn Problem). Prove or disprove the following conjecture: Vanishing of the Landsberg curvature implies that the metric is Berwald.Problem 2. Describe 2-dimensional Finlser metrics admitting 2- and 3- dimensional pseudogroup of projective transformations.Problem 3. Prove or disprove the following conjecture: on a closed surface of negative Euler characteristic two projectively equivalent Finsler metrics are trivially projectively equivalent.

我们的目标是解决Finlser几何中的以下三个问题：问题1 （Landsberg Unicorn Problem）。证明或证伪下列猜想：兰氏曲率的消失意味着度规是伯瓦尔德度规。问题2。描述二维芬瑟度量允许二维和三维伪群的射影变换。问题3。证明或反驳以下猜想：在负欧拉特征的封闭曲面上，两个射影等价的芬斯勒度量是平凡射影等价的。

项目成果

Projectively equivalent Finsler metrics on surfaces of negative Euler characteristic

负欧拉特征曲面上的投影等效 Finsler 度量

• DOI: 10.1142/s1793525320500491
• 发表时间: 2022
• 期刊: Journal of Topology and Analysis
• 影响因子: 0.8
• 作者: Julius

Conformally related Douglas metrics in dimension two are Randers

第二维中保形相关的道格拉斯度量是 Randers

• DOI: 10.1007/s00013-020-01533-5
• 发表时间: 2021
• 期刊: Archiv der Mathematik
• 影响因子: 0.6
• 作者: Matveev;Vladimir S;Saberali;Samaneh
• 通讯作者: Samaneh

Almost All Finsler Metrics have Infinite Dimensional Holonomy Group

几乎所有芬斯勒度量都有无限维完整群

• DOI: 10.1007/s12220-020-00517-9
• 发表时间: 2021
• 期刊: The Journal of Geometric Analysis
• 作者: Hubicska;Matveev;Muzsnay
• 通讯作者: Muzsnay

On Finsler surfaces that are both Douglas and generalized Berwald

在 Finsler 曲面上，既是 Douglas 曲面，又是广义 Berwald 曲面

• DOI: 10.5486/pmd.2020.8784
• 发表时间: 2020
• 期刊: Publicationes Mathematicae Debrecen
• 影响因子: 0.6
• 作者: Bartelmess;Julius
• 通讯作者: Julius

Finsler metrics on surfaces admitting three projective vector fields

• DOI: 10.1016/j.difgeo.2019.101590
• 发表时间: 2019-08
• 期刊: Differential Geometry and its Applications
• 影响因子: 0.5
• 作者: J. Lang