Some Ricci-Flat $(α,β)$-Metrics

In this paper, we study a special class of Finsler metrics, $(α,β)$-metrics, defined by $F = αϕ(\fracβα)$, where $α$ is a Riemannian metric and $β$ is a 1-form. We find an equation that characterizes Ricci-flat $(α,β)$-metrics under the condition that the length of $β$ with respect to $α$ is constant.

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