The Finslerian version of the Nash embedding theorem

Question

Is it true to say that every Finslerian manifold can be isometrically embedded in some $M_{n}(\mathbb{R})$ with operator norm?

Note that every Riemannian manifold can be embedded in some matrix space isometrically, since the matrix space contains a copy of the standard $\mathbb{R}^{n}$:

Hilbert-irreducible Banach space

Answer 1

Burago and Ivanov have shown that any compact Finsler manifold can be isometrically embedded into a finite-dimensional normed space. They also furnish examples of non-compact Finsler manifolds that can not be isometrically embedded in any finite-dimensional normed space.