A local classification of a class of \((\alpha ,\beta )\) metrics with constant flag curvature (Q960870)

In Finsler geometry, flag curvature represents a generalization of the notion of sectional curvature from Riemannian geometry. This paper completes the local classification of (\(\alpha , \beta \)) metrics of the type \(F=\alpha(1+{{\beta}\over{\alpha}})^2 \), with constant flag curvature. The author proves that if such a metric has constant flag curvature, then the Finsler space must be locally projectively flat. Then, he studies another class of (\(\alpha , \beta \)) metrics with \(F=\alpha(1+{{\beta}\over{\alpha}})^p, |{p}|>1 \). He obtains that there are no non-trivial Matsumoto metrics (called a slope of the mountain) with constant flag curvature.