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Journals / Turkish Journal of Mathematics / 2012 / Cilt: 36 - Sayı: 3

Generalized Berwald metrics

Esmaeil PEYGHAN
Akbar TAYEBI
Pages
475–484
Publication Date
2022-11-05
DOI
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AI Summary & Key Takeaways

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

Then we prove that on generalized Berwald metrics, the notions of generalized Landsberg and Landsberg curvatures are equivalent.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we consider a class of Finsler metrics called generalized Berwald metrics which contains the class of Berwald metrics as a special case.
📊
Key Findings & Data:We prove that every generalized Berwald metrics with non-zero scalar flag curvature or isotropic Berwald curvature is a Randers metric.
💡
Conclusion & Impact:Then we prove that on generalized Berwald metrics, the notions of generalized Landsberg and Landsberg curvatures are equivalent.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Berwald metric · landsberg metric · randers metric

Abstract

In this paper, we consider a class of Finsler metrics called generalized Berwald metrics which contains the class of Berwald metrics as a special case. We prove that every generalized Berwald metrics with non-zero scalar flag curvature or isotropic Berwald curvature is a Randers metric. Then we prove that on generalized Berwald metrics, the notions of generalized Landsberg and Landsberg curvatures are equivalent.

Özet

In this paper, we consider a class of Finsler metrics called generalized Berwald metrics which contains the class of Berwald metrics as a special case. We prove that every generalized Berwald metrics with non-zero scalar flag curvature or isotropic Berwald curvature is a Randers metric. Then we prove that on generalized Berwald metrics, the notions of generalized Landsberg and Landsberg curvatures are equivalent.

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Cite This Article

PEYGHAN, E., TAYEBI, A. (2022). Generalized Berwald metrics. Turkish Journal of Mathematics, Cilt: 36 - Sayı: 3, 475–484. https://ajindex.com/articles/608411

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