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Some non-Riemannian curvature properties of the new class of \((\alpha , \beta )\)-metrics

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Abstract

In this paper, we study some important non-Riemannian curvature properties of the new class of \( (\alpha ,\beta ) \)-metrics introduced by Pişcoran–Mishra in Finsler geometry. We prove that this class of Finsler metrics are Landsbergian if and only if they are weakly Landsbergian if and only if they are Berwaldian. Then, we show that this class of Finsler metrics has vanishing \(\Xi \)-curvature if and only if they have vanishing S-curvature \(\textbf{S}=0\). Finally, we show that this class of Finsler metrics has almost vanishing H-curvature if and only if \(\textbf{H}=0\).

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Authors and Affiliations

  1. Department of Mathematics, Basic Sciences Faculty, University of Bonab, Bonab, Iran

    Jila Majidi & Ali Haji-Badali

  2. Department of Mathematics, Faculty of Science, University of Qom, Qom, Iran

    Akbar Tayebi

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  1. Jila Majidi
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  2. Akbar Tayebi
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  3. Ali Haji-Badali
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Correspondence to Ali Haji-Badali.

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Majidi, J., Tayebi, A. & Haji-Badali, A. Some non-Riemannian curvature properties of the new class of \((\alpha , \beta )\)-metrics. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 118, 78 (2024). https://doi.org/10.1007/s13398-024-01580-5

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  • DOI: https://doi.org/10.1007/s13398-024-01580-5

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