Three-sphere
= Three-sphere
{title2=$S^3$}
= 3-sphere
{c}
{synonym}
The three-sphere is the unit sphere in four-dimensional <Euclidean space>:
$$
S^3=\{x\in\mathbb R^4:\lVert x\rVert=1\}.
$$
Identifying $\mathbb R^4$ with $\mathbb C^2$ realizes it as $\{(z_1,z_2):|z_1|^2+|z_2|^2=1\}$.