New classes of Finsler metrics: The birth of new projective invariant

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2025-04-14 DOI:10.1016/j.difgeo.2025.102250

Nasrin Sadeghzadeh

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引用次数: 0

Abstract

This paper presents a pioneering projective invariant in Finsler geometry, introducing a new class of Finsler metrics that are preserved under projective transformations. The newly formulated weakly generalized Douglas-Weyl

(W - G D W)

equation facilitates the generalization of generalized Douglas-Weyl

(G D W)

-metrics into the broader category of

W - G D W

-metrics, which encompasses all GDW-metrics. Within this class, there are also two additional subclasses: generalized weakly-Weyl metrics, characterized by a milder form of Weyl curvature, and generalized

\tilde{D}

-metrics, defined by a less strict version of Douglas curvature. The paper provides a comprehensive overview of these generalized class of Finsler metrics and elucidates their properties, supported by detailed examples.

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芬斯勒度量的新类别：新射影不变量的诞生

本文提出了芬斯勒几何中的一个开创性的射影不变量，引入了一类新的在射影变换下保持的芬斯勒度量。新建立的弱广义Douglas-Weyl （W−GDW）方程有助于将广义Douglas-Weyl (GDW)-度量推广到更广泛的W−GDW-度量范畴，其中包括所有GDW-度量。在这类中，还有两个额外的子类：广义弱Weyl度量，以温和形式的Weyl曲率为特征，广义D ~度量，由不严格版本的道格拉斯曲率定义。本文全面概述了这类广义的芬斯勒度量，并举例说明了它们的性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.