ON CUBIC (\alpha, \beta)-METRICS IN FINSLER GEOMETRY

Hosein Tondro Vishkaei, Akbar Tayebi

DOI Number
https://doi.org/10.22190/FUMI220323030T
First page
439
Last page
452

Abstract


In this paper, we study the class of  cubic (\alpha, \beta)-metrics.  We show that every  weakly Landsberg cubic (\alpha, \beta)-metric has vanishing S-curvature. Using it, we prove that  cubic (\alpha, \beta)-metric is a weakly Landsberg metric if and only if it is a Berwald metric. This yields an extension of the  Matsumoto's result for Landsberg cubic metric.

Keywords

Cubic metric, weakly Landsberg metric, S-curvature

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References


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DOI: https://doi.org/10.22190/FUMI220323030T

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