Finsler manifold

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

• $F(v+w) \leq F(v)+F(w)$ for $v,w\in T_x M$.

• $F(\lambda v)=\lambda F(v)$ for $\lambda \geq 0$.

• $F(v)>0$ unless $v=0$.

See wikipedia.

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

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Author of the notes: Antonio J. Pan-Collantes

antonio.pan@uca.es