1. Let p be an arbitrary point on the unit sphere S2n+1 of Cn+1=R2n+2. Determine the tangent space TpS2n+1 and show that it contains an n-dimensional complex subspace of Cn+1 2. Relevant equations 3. It is easy to find tangent space of S1; it is only tangent vector field of S1. But what must do for higher dimension and how can I show it contains an n-dimensional subspace of Cn+1. Thanks for your helps.