Journal of Mathematical Physics, Analysis, Geometry
2021, vol. 17, No 4, pp. 468-483   https://doi.org/10.15407/mag17.04.468     ( to contents , go back )
https://doi.org/10.15407/mag17.04.468

On Landsberg Warped Product Metrics

Mehran Gabrani

Department of Mathematics, Faculty of Science, Urmia university, Urmia, Iran
E-mail: m.gabrani@urmia.ac.ir

Bahman Rezaei

Department of Mathematics, Faculty of Science, Urmia university, Urmia, Iran
E-mail: b.rezaei@urmia.ac.ir

Esra Sengelen Sevim

Department of Mathematics, Istanbul Bilgi University, 34060, Eski Silahtaraga Elektrik Santrali, Kazim Karabekir Cad. No: 2/13 Eyupsultan, Istanbul, Turkey
E-mail: esra.sengelen@bilgi.edu.tr

Received September 2, 2020, revised December 4, 2020.

Abstract

In this paper, we discuss a class of Finsler metrics which are called Finsler warped product metrics. These metrics have been studied by Chen-Shen- Zhao, 2018. Basically, we study the Berwald curvature of Finsler warped product metrics. Also, we characterize the Finsler warped product metrics of isotropic Berwald curvature, then we obtain that they are Randers metrics (Theorem 1.2). Moreover, we consider an important problem which is unicorn problem in Finsler geometry for the class of Finsler metrics. In fact, we get the answer of the crucial question of this study that whether or not such a Landsberg Finsler warped product metric is a Berwald metric (Theorem 1.3).

Mathematics Subject Classification 2010: 53B40, 53C60
Key words: Finsler warped product metric, Landsberg metric, isotropic Berwald curvature

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