TITLE: The Finslerian version of the Nash embedding theorem
QUESTION [10 upvotes]: 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

REPLY [12 votes]: 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.