A Geometric characterization of Finsler manifolds of constant curvature K=1

Abstract

We prove that a Finsler manifold 𝔽m is of constant curvature K=1 if and only if the unit horizontal Liouville vector field is a Killing vector field on the indicatrix bundle IM of 𝔽m.

Keywords

• Finsler manifold of constant curvature
• Killing vector field
• indicatrix bundle
• horizontal Liouville vector field.