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

Document Type : Original Article

Authors

Bankteshwar Tiwari ¹

Ranadip Gangopadhyay ¹

Ghanashyam Kr. Prajapati ²

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

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

10.22034/kjm.2019.84205

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.

Keywords

Finsler space

General (α, β)-metric

Ξ-curvature

$H$-curvature

Subjects

• 53 Differential geometry

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