Finsler manifold

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

$F (v + w) \leq F (v) + F (w)$ for $v, w \in T_{x} M$ .
$F (λ v) = λ F (v)$ for $λ \geq 0$ .
$F (v) > 0$ unless $v = 0$ .
See Wikipedia.

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