Abstract:

In this article, the author studies the projectively flat Matsumoto metric F=α²/(α-β), where α=\sqrt{a_{ij}y^{i}y^{j}} is a Riemannian metric and β=b_iyⁱ is a 1-form. They conclude that α is locally projectively flat and β is paralled with respect to α. And get the same result for the higher order approximate Matsumoto metric.

Key words: Matsumoto metric, projectively flat, (α,β)-metric