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arXiv · 1706.07944

Some curvature properties of Cartan spaces with mth root metrics

Akbar Tayebi·Ali Nankali·Esmaeil Peyghan
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Abstract

In this paper, we prove that every m-th root metric with isotropic mean Berwald curvature reduces to a weakly Berwald metric. Then we show that an m-th root metric with isotropic mean Landsberg curvature is a weakly Landsberg metric. We find necessary and sufficient condition under which conformal $\beta$-change of an m-th root metric be locally dually flat. Finally, we prove that the conformal $\beta$-change of locally projectively flat m-th root metrics are locally Minkowskian.

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Akbar Tayebi, Ali Nankali, Esmaeil Peyghan. 2017-06-24. Some curvature properties of Cartan spaces with mth root metrics. https://arxiv.org/abs/1706.07944

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