Projectively flat cubic (α, β)-metric with constant flag curvature K = 0

Abstract

Finsler metrics with straight geodesics on an open subset in Rn are thought to be projective. The flag curvature of any projective Finsler metric is known to be a scalar function of tangent vectors (the flag curvature must be a constant if it is Riemannian). We categorize locally projectively flat cubic (α, β)-metric with constant Ricci curvature and obtain cubic (α, β)-metric of zero flag curvature.

Keywords

• finsler space
• projective change
• cubic (α
• β)-metric
• projective flatness
• flag curvature