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Sphere

{title2=$S^n$}

The unit sphere $S^n\subseteq\mathbb R^{n+1}$ is the regular level set $\lVert x\rVert^2=1$. Its tangent space is
$$
T_xS^n=x^\perp=\{v\in\mathbb R^{n+1}:x\mathbin\cdot v=0\}.
$$


Unit sphere as a regular level set

Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 1 / 26H / a / Solution

Unit sphere as a regular level set ( $S^{n}$ )

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Unit sphere as a regular level set (Sn)

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