As of the Wikipedia article on principal bundles connections:

Let $\pi: P \to M$ be a smooth principal bundle, a principal $G$-bundle over a smooth manifold $M$. Then a

principal $G$-connectionon $P$ is a differential $1$-form on $P$ with values in the Lie algebra $\mathfrak g$ of $G$ which is $G$-equivariant and reproduces the Lie algebra generators of the fundamental vector fields on $P$.

Now for the principal $U_1$-bundle $S^{2N+1} \to CP^N$, I appear to have shown that it does not admit a principal $U_1$-connection. Is this true, or a load of rudbbish?

P.S. My "proof" also implies that there is a unique connection form for the $U_{N-1}$-bundle $SU_{N} \to CP^{N-1}$. Can I assume that this is also incorrect?