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arXiv · 2011.12778

On $(\alpha, \beta, \gamma)$-metrics

Nasrin Sadeghzadeh·Tahere Rajabi
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Abstract

In this paper, a new class of Finsler metrics which are included $(\alpha,\beta)$-metrics are introduced. They are defined by a Riemannian metric and two 1-forms $\beta=b_i(x)y^i$ and $\gamma= \gamma_i(x)y^i$. This class of metrics are a generalization of $(\alpha,\beta)$-metrics which are not always $(\alpha,\beta)$-metric. We find a necessary and sufficient condition for this metric to be locally projectively flat and then we prove the conditions for this metric to be of Douglas type.

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Nasrin Sadeghzadeh, Tahere Rajabi. 2020-11-22. On $(\alpha, \beta, \gamma)$-metrics. https://arxiv.org/abs/2011.12778

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