On the projective algebra of first approximate matsumoto metric

In the present paper, we have introduce a special metric, called First Approximate Matsumoto metric is analyzed as a certain on an n dimensional space with the projective Algebra and Lie Algebra of the projective group and this metric is characterized as certain Lie sub algebra of the projective algebra. Further, which is devoted to studying the condition of Finsler space of constant flag curvature and vanishing S curvature admits a non Riemannian space of affine projective vector field with First Approximate Matsumoto metric is Berwald space.