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Journals / International Electronic Journal of Geometry / 2025 / Volume: 18 Issue: 2

On the Geometry of the Indicatrix Bundle of a Finsler Manifold

Mohamed Tahar Kadaoui Abbassi(Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Benabdellah University)0000-0001-7802-0624
Abderrahim Mekrami(Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University)0009-0002-5843-5026
Pages
—
Publication Date
2025-10-19
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Furthermore, we provide a characterization of Finsler manifolds with positive constant flag curvature via the existence of $K$-contact structures on their indicatrix bundles.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, we investigate a class of metrics induced by $F$-natural metrics on the indicatrix bundle of a Finsler manifold.
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Key Findings & Data:This class constitutes a four-parameter family that generalizes the well-known $g$-natural metrics on the unit tangent bundle of a Riemannian manifold.
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Conclusion & Impact:Furthermore, we provide a characterization of Finsler manifolds with positive constant flag curvature via the existence of $K$-contact structures on their indicatrix bundles.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Finsler structure · indicatrix bundle · $F$-natural metric

Abstract

In this paper, we investigate a class of metrics induced by $F$-natural metrics on the indicatrix bundle of a Finsler manifold. This class constitutes a four-parameter family that generalizes the well-known $g$-natural metrics on the unit tangent bundle of a Riemannian manifold. Within this framework, we construct a three-parameter family of contact metric structures whose associated metrics are $F$-natural, and we establish that, in contrast to the Riemannian case —where all such $K$-contact metrics on unit tangent bundles are necessarily Sasakian— the corresponding structures in the Finslerian setting can be $K$-contact without being Sasakian. Furthermore, we provide a characterization of Finsler manifolds with positive constant flag curvature via the existence of $K$-contact structures on their indicatrix bundles.

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Cite This Article

Abbassi, M. T. K., Mekrami, A. (2025). On the Geometry of the Indicatrix Bundle of a Finsler Manifold. International Electronic Journal of Geometry, Volume: 18 Issue: 2. https://doi.org/10.36890/iejg.1676428

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