• 제목/요약/키워드: Matsumoto

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WEAKLY BERWALD SPACE WITH A SPECIAL (α, β)-METRIC

  • PRADEEP KUMAR;AJAYKUMAR AR
    • 호남수학학술지
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    • 제45권3호
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    • pp.491-502
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    • 2023

  • As a generalization of Berwald spaces, we have the ideas of Douglas spaces and Landsberg spaces. S. Bacso defined a weakly-Berwald space as another generalization of Berwald spaces. In 1972, Matsumoto proposed the (α, β) metric, which is a Finsler metric derived from a Riemannian metric α and a differential 1-form β. In this paper, we investigated an important class of (α, β)-metrics of the form $F={\mu}_1\alpha+{\mu}_2\beta+{\mu}_3\frac{\beta^2}{\alpha}$, which is recognized as a special form of the first approximate Matsumoto metric on an n-dimensional manifold, and we obtain the criteria for such metrics to be weakly-Berwald metrics. A Finsler space with a special (α, β)-metric is a weakly Berwald space if and only if Bmm is a 1-form. We have shown that under certain geometric and algebraic circumstances, it transforms into a weakly Berwald space.

  • https://doi.org/10.5831/HMJ.2023.45.3.491 인용 PDF

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