Golden Finsler Geometry: Local Properties and Global Deformations

Abstract

We introduce the concept of a golden Finsler structure on a finite-dimensional smooth manifold $M$ and investigate it from both local (coordinate-based) and global (coordinate-free) perspectives. Locally, we explicitly compute the fundamental metric tensor, establish the positive definiteness condition, and derive the geodesic spray coefficients. Furthermore, we investigate the projective flatness of the golden $(α, β)$-metric and prove the non-existence of almost rational golden $(α, β)$-metrics. Globally, we define the golden Finsler change $\widetilde{F}$ of a base Finsler metric $F$ and examine its geometric properties utilizing a special concurrent $π$-vector field. We explicitly determine how fundamental non-linear structures, including the Barthel and Berwald connections, transform under this change. Finally, we prove that $\widetilde{F}$ and $F$ cannot be projectively related.

Disclosure

“entz-violation would theoretically break down. Therefore, our results provide a rigorous structural founda- tion for future applications of golden Finsler manifolds in both differential geometry and theoretical physics. Declarations • Generative AI and AI-assisted technologies in the manuscript prepa- ration process: During the preparation of this work the authors used Google Gemini in order to refine the language and improve the structural flow of the text. After usin”

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2026-08-23T18:54:28.626829Z

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