Generalized Weakly-Weyl Finsler Metrics: A Generalized Approach to Sakaguchi's Theorem
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909895933034496 |
|---|---|
| author | Sadeghzadeh, Nasrin Yavari, Meshkat |
| author_facet | Sadeghzadeh, Nasrin Yavari, Meshkat |
| contents | The development of projective invariant Weyl metrics in this paper offers a fresh perspective, as we establish the characteristics of both weakly-Weyl and generalized weakly-Weyl Finsler metrics. We thoroughly examine the connections between these metrics and various projective invariants, highlighting their significance in the context of generalized Sakaguchi's Theorem, which states that every Finsler metric of scalar flag curvature is a GDW-metric. Additionally, we introduce several illustrative examples pertaining to this new class of projective invariant Finsler metrics. Specifically, we explore the category of weakly-Weyl spherically symmetric Finsler metrics in $\mathbb{R}^n$. Importantly, we demonstrate that the two classes weakly-Weyl and $W$-quadratic spherically symmetric Finsler metrics in $\mathbb{R}^n$ are equivalent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06916 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Weakly-Weyl Finsler Metrics: A Generalized Approach to Sakaguchi's Theorem Sadeghzadeh, Nasrin Yavari, Meshkat Differential Geometry 53B40, 53C60 The development of projective invariant Weyl metrics in this paper offers a fresh perspective, as we establish the characteristics of both weakly-Weyl and generalized weakly-Weyl Finsler metrics. We thoroughly examine the connections between these metrics and various projective invariants, highlighting their significance in the context of generalized Sakaguchi's Theorem, which states that every Finsler metric of scalar flag curvature is a GDW-metric. Additionally, we introduce several illustrative examples pertaining to this new class of projective invariant Finsler metrics. Specifically, we explore the category of weakly-Weyl spherically symmetric Finsler metrics in $\mathbb{R}^n$. Importantly, we demonstrate that the two classes weakly-Weyl and $W$-quadratic spherically symmetric Finsler metrics in $\mathbb{R}^n$ are equivalent. |
| title | Generalized Weakly-Weyl Finsler Metrics: A Generalized Approach to Sakaguchi's Theorem |
| topic | Differential Geometry 53B40, 53C60 |
| url | https://arxiv.org/abs/2511.06916 |