Finsler manifold

A Finsler manifold is a differentiable manifold $M$ together with a Finsler metric, which is a continuous non-negative function $F:TM\to [0,+\infty )$ defined on the tangent bundle so that for each point $x$ of $M$:

• $F(v+w)\le F(v)+F(w)$ for $v,w\in T_{x}M$.
• $F(\lambda v)=\lambda F(v)$ for $\lambda \ge 0$.
• $F(v)>0$ unless $v=0$.
  See Wikipedia.

Riemannian manifolds (but not pseudo-Riemannian manifolds) are special cases of Finsler manifolds.