Finsler manifold

Summary

A Finsler manifold is a smooth manifold with a smoothly varying, strongly convex norm-like function on each tangent space. It generalises a Riemannian manifold, where the length of a tangent vector comes from an inner product. Lengths of curves, distances and geodesics are defined as in Riemannian geometry. But the unit ball in each tangent space may be any smooth strongly convex body, not only an ellipsoid.