On Zermelo's navigation problem and weighted Einstein Randers metrics
This paper investigates a specific form of weighted Ricci curvature known as the quasi-Einstein metric. Two Finsler metrics, $F$ and $\tilde{F}$ are considered, which are generated by navigation representations $(h, W)$ and $(F, V)$, respectively, where $W$ represents a vector field, and $V$ represe...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Amirkabir University of Technology
2025-07-01
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| Series: | AUT Journal of Mathematics and Computing |
| Subjects: | |
| Online Access: | https://ajmc.aut.ac.ir/article_5403_144efee6fb7c3825880bbdc1ade66406.pdf |
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| Summary: | This paper investigates a specific form of weighted Ricci curvature known as the quasi-Einstein metric. Two Finsler metrics, $F$ and $\tilde{F}$ are considered, which are generated by navigation representations $(h, W)$ and $(F, V)$, respectively, where $W$ represents a vector field, and $V$ represents a conformal vector field on the manifold $M$. The main focus is on identifying the necessary and sufficient condition for the Randers metric $F$ to qualify as a quasi-Einstein metric. Additionally; we establish the relationship between the curvatures of the given Finsler metrics $F$ and $\tilde{F}$. |
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| ISSN: | 2783-2449 2783-2287 |