Nonvanishing tangent field on an odd-dimensional sphere
= Nonvanishing tangent field on an odd-dimensional sphere
{title2=$V(x)=Jx$}
Identify $\mathbb R^{2m+2}$ with $\mathbb C^{m+1}$ and let $J$ be multiplication by $i$. On the unit sphere $S^{2m+1}$, the <vector field> $V(x)=Jx$ has norm one and satisfies $\langle x,Jx\rangle=0$. It is therefore a continuous tangent <nowhere-zero section>, including on $S^1$.