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

Generalized Berwald metrics

Esmaeil PEYGHAN
Akbar TAYEBI
Sayfa
475–484
Yayın Tarihi
2022-11-05
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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.
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Temel Bulgular & Veri:We prove that every generalized Berwald metrics with non-zero scalar flag curvature or isotropic Berwald curvature is a Randers metric.
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Sonuç & Katkı:Then we prove that on generalized Berwald metrics, the notions of generalized Landsberg and Landsberg curvatures are equivalent.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Berwald metric · landsberg metric · randers metric

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.

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.

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Bu Makaleye Atıf Yap

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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Kaynakça (17)

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  17. Tayebi, A., Peyghan, E.: On special Berwald metrics, Symmetry, Integrability and Geometry: Methods and its Applications, 6 (2010), 008, 9 page. Tayebi, A., RaŞe. Rad, M.: S-curvature of isotropic Berwald metrics, Science in China, Series A: Mathematics., 2198–2204 (2008). Esmaeil PEYGHAN Department of Mathematics, Faculty of Science Arak University, Arak, 38156-8-8349, IRAN e-mail: [email protected] Akbar TAYEBI Department of Math