论三次(\alpha, \beta)-芬斯勒几何中的度量

IF 0.5 Q3 MATHEMATICS Facta Universitatis-Series Mathematics and Informatics Pub Date : 2022-08-06 DOI:10.22190/fumi220323030t

Hosein Tondro Vishkaei, A. Tayebi

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摘要

在本文中，我们研究了一类三次(\alpha, \beta)-度量。我们证明了每一个弱Landsberg立方(\alpha, \beta)度规都具有消失的s曲率。利用它，我们证明了三次(\alpha, \beta)度规是弱Landsberg度规当且仅当它是Berwald度规。这就得到了对Landsberg三次度规的Matsumoto结果的扩展。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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.

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Facta Universitatis-Series Mathematics and Informatics MATHEMATICS-

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