On General $( \alpha, \beta)$-Metrics with Some Curvature Properties

Document Type: Original Article

Authors

1 DST-CIMS, Institute of Science, Banaras Hindu University, Varanasi-221005, India.

2 Loknayak Jai Prakash Institute of Technology, Chhapra-841302, India.

Abstract

In this paper, we study a class of Finsler metric called general $(\alpha, \beta)$ metrics and obtain an equation that characterizes these Finsler metrics of almost vanishing H-curvature. As a consequence of this result, we prove that a general $(\alpha, \beta)$-metric has almost vanishing $H$-curvature if and only if it has almost vanishing $\Xi$-curvature.

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