WEAKLY BERWALD SPACE WITH $(\alpha,\beta)$-METRIC

Résumé

Douglas spaces and Landsberg spaces are regarded as generalizations of Berwald spaces. S. Bacso proposed weakly Berwald space as one more general form of it.
This paper provides a detailed insight into the verification of the conditions of a weakly Berwald space under which a Finsler space equipped with an special
$(\alpha, \beta)$-metric of the form $L(\alpha, \beta) = c_1 \alpha + c_2 \beta + \frac{\alpha^2}{\beta}$ reduces to a weakly-Berwald space,
here $\alpha$ denotes Riemannian metric and $\beta$ denotes differential 1-form.