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Let $E$ be a Riemannian vector bundle over a manifold. Can $E$ be considered as a trivial subbundle of trivial bundle$M\times \mathbb{R}^n$ for some $n$ such that the metric of each fiber is the restriction of Euclidean metric of $\mathbb{R}^n$?
Let $E$ be a Riemannian vector bundle over a manifold. Can $E$ be considered as a trivial subbundle $M\times \mathbb{R}^n$ for some $n$ such that the metric of each fiber is the restriction of Euclidean metric of $\mathbb{R}^n$?
Let $E$ be a Riemannian vector bundle over a manifold. Can $E$ be considered as a subbundle of trivial bundle$M\times \mathbb{R}^n$ for some $n$ such that the metric of each fiber is the restriction of Euclidean metric of $\mathbb{R}^n$?
A vector bundle analogy of the Nash embedding theorem
Let $E$ be a Riemannian vector bundle over a manifold. Can $E$ be considered as a trivial subbundle $M\times \mathbb{R}^n$ for some $n$ such that the metric of each fiber is the restriction of Euclidean metric of $\mathbb{R}^n$?
