Generalized P-Reducible $(\alpha, \beta)$-Metrics with Vanishing S-curvature

A. Tayebi; H. Sadeghi

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arXiv · 1510.07989

Generalized P-Reducible $(\alpha, \beta)$-Metrics with Vanishing S-curvature

A. Tayebi·H. Sadeghi

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Abstract

In this paper, we study one of the open problems in Finsler geometry which presented by Matsumoto-Shimada about the existence of P-reducible metric which is not C-reducible. For this aim, we study a class of Finsler metrics called generalized P-reducible metrics that contains the class of P-reducible metrics. We prove that every generalized P-reducible $(\alpha, \beta)$-metric with vanishing S-curvature reduces to a Berwald metric or C-reducible metric. It results that there is not any concrete P-reducible $(\alpha,\beta)$-metric with vanishing S-curvature.

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BibTeX RIS

A. Tayebi, H. Sadeghi. 2015-10-26. Generalized P-Reducible $(\alpha, \beta)$-Metrics with Vanishing S-curvature. https://arxiv.org/abs/1510.07989

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