Show that any affine connection $nabla$ on $mathbb{R}^n$ is of the form $nabla=D+Gamma$.
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Show that any affine connection $nabla$ on $mathbb{R}^n$ is of the form $nabla=D+Gamma$ , where $D$ is the Euclidean connection and $Gamma:mathcal{X}(mathbb{R}^n) times mathcal{X}(mathbb{R}^n) rightarrow mathcal{X}(mathbb{R}^n)$ is any $C^{infty}(mathbb{R}^n)$ -bilinear map. Showing that $D+Gamma$ is an affine connection is easy, but I don't know how to show the converse. I mean, what's special about $mathbb{R}^n$ ?
manifolds riemannian-geometry vector-fields connections
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asked Nov 21 at 21:49
bbw
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