In this paper, we study the well-known unicorn problem for Finsler metrics. First, prove that every homogeneous Landsberg surface has isotropic flag curvature. Then by using particular form of curvature, a rigidity result on surfaces. Indeed, is Riemannian or locally Minkowskian. Thus, give an affirmative answer to Xu-Deng's conjecture in two-dimensional manifolds.

In this article, we report several new geometric and Lyapunov characterizations of incrementally stable systems on Finsler Riemannian manifolds. A intrinsic proof an important theorem in contraction analysis is given via the complete lift system. Based this, two are derived, namely, converse theorems, revelation connection between incremental stability equilibrium point, which second result rec...

The broken scattering relation consists of the total lengths geodesics that start from boundary, change direction once inside manifold, and propagate to boundary. We show if two reversible Finsler manifolds satisfying a convex foliation condition have same relation, then they are isometric. This implies some anisotropic material parameters Earth can be in principle reconstructed single measurem...