- #1

Lee33

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Define the map ##\pi : (\mathbb{R}^3-\{(0,0,0)\})\to S^2## by ##\pi(p)=\frac{p}{||p||}.## Show that if ##\Sigma_R## is the sphere of radius ##R>0##, then the Gauss map of ##\Sigma_R## is ##\pi|_{\Sigma_R}## (which means the map ##\pi## restricted to the surface ##\Sigma_R##.) Compute the shape operator and the Gauss curvature of the sphere.

I don't even know where to start?