Unicorn metrics with almost vanishing ${\bf H}$- and ${\bf \Xi}$-curvatures

Authors: AKBAR TAYEBI, Tayebeh TABATABAEIFAR

Abstract: In this paper, we consider a class of almost regular $(\alpha, \beta)$-metrics constructed by Shen called unicorn metrics. First, we prove that every unicorn metric with almost vanishing ${\bf H}$-curvature is a Berwald metric. Then we show that every unicorn metric with almost vanishing $\Xi$-curvature reduces to a Berwald metric.

Keywords: Unicorn metric, the non-Riemannian quantity ${\bf H}$, almost vanishing ${\bf \Xi}$-curvature

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