# Deicke's theorem

From Diffgeom

Template:Finsler metric result

## Statement

Let be a Finsler manifold. Let be a point. The norm in the tangent space at is a Euclidean norm if and only if the mean Cartan torsion is 0 for all tangent vectors at .

Note that for a Riemannian metric, the norm is Euclidean on each tangent space, and the mean Cartan torsion is identically zero.