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arXiv · 2510.02344

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

Nasrin Sadeghzadeh
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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 $G D W$-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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BibTeXRIS

Nasrin Sadeghzadeh. 2025-09-27. New classes of Finsler metrics: The birth of new projective invatiant. https://doi.org/10.1016/j.difgeo.2025.102250

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