## deforming manifolds in $\mathbb{C}^n$ [closed]

I have found that arbitrary real n-spheres cannot be contracted to a point, at least that's what I found on wiki. But I am wondering if a manifold in $\mathbb{C}^n$ given by $|z_1|^2 + |z_2|^2 + ... + |z_n|^2 =1$ can be deformed continuously into one of the z's on the manifold, say, $z_{n'}$. Is such a deformation possible?

The "contractibility" of a space does not need mention of an ambient space that it lies in... your sphere can be in complex space or real space, but they are both topologically your standard $S^n$, which is not contractible (unless $n=\infty$). In any case, this question is not appropriate for this forum; try math.stackexchange.com – Chris Gerig Jan 12 2012 at 7:47