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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

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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.

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    $\begingroup$ @T.Amdehberhan very interesting thanks $\endgroup$ – Ali Taghavi Oct 30 '16 at 21:04

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